Labs_Digital Logic Design Manual

Lab Manual, Digital Logic Design

Exp # 1.

FAMILIARIZATION WITH DIGITAL LOGIC TRAINER

Logi Logicc Tr Trai aine nerr is a devic devicee which which is used used to stud study y inte intera ract ctio ion n of diff differe erent nt logi logicc and and universal gates.

Figure 1: NB-09 Digital Logic Trainer

Complete description of NB-09 Digital Logic Trainer shown in figure 1 is described below “A” Section A comprises of DC Jack for the power supply adaptor. “B” Section B consists of “8 BIT LED OUTPUT INDICATOR “. The bulb in this section glows when there is logic 1 and remains off when there is logic 0. -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 1


“D” Section D consists of “AND GATES”. It is a basic combinational logic device where all inputs must b high for the output to be high. “E” Section E comprises of “OR GATES” It is a basic combination logic device where the output goes high when any or two input will be high. “F” Section F consists of “NAND GATES”. It is a basic combinational logic device where all inputs must be high for output to be low. It is invert of AND GATE. “G” Section G consists of “NOR GATES” it is a basic combinational logic device where all inputs must be low for output to be high. A NOT OR circuit. It is invert of OR. Its meaning No OR. “H” Section H consists of “XOR GATES” it is basic combinational logic device where an odd number of high inputs generates a high output.

“I” Section I consists of “NOT GATES” it is a basic combinational logic device where the output is always the opposite from the input. It is also called an inverter. “J” Section Section J consists consists of “VOLTAGE SECTION” SECTION” one port is of +5V, the other is for ground connection and the third is of -5V. Also Section J consists of “VOLTAGE SECTION” one port is of +15V, the other is for ground connection and the third is of -15V. “L” Section L consists of PULSE. It can be generator a pulse of 1 second, 0.1 second and 0.01 second. “M” Section M consists of DATA SWITCHES. There are five data switches in this trainer and have four there test point in their correspondence. “N” Sectio Section n N consist consistss of “SOLDE “SOLDER R LESS LESS BREADB BREADBOAR OARD D OR PROTO PROTO BOARD” BOARD” It is consisting of so many holes.

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“D” Section D consists of “AND GATES”. It is a basic combinational logic device where all inputs must b high for the output to be high. “E” Section E comprises of “OR GATES” It is a basic combination logic device where the output goes high when any or two input will be high. “F” Section F consists of “NAND GATES”. It is a basic combinational logic device where all inputs must be high for output to be low. It is invert of AND GATE. “G” Section G consists of “NOR GATES” it is a basic combinational logic device where all inputs must be low for output to be high. A NOT OR circuit. It is invert of OR. Its meaning No OR. “H” Section H consists of “XOR GATES” it is basic combinational logic device where an odd number of high inputs generates a high output.

“I” Section I consists of “NOT GATES” it is a basic combinational logic device where the output is always the opposite from the input. It is also called an inverter. “J” Section Section J consists consists of “VOLTAGE SECTION” SECTION” one port is of +5V, the other is for ground connection and the third is of -5V. Also Section J consists of “VOLTAGE SECTION” one port is of +15V, the other is for ground connection and the third is of -15V. “L” Section L consists of PULSE. It can be generator a pulse of 1 second, 0.1 second and 0.01 second. “M” Section M consists of DATA SWITCHES. There are five data switches in this trainer and have four there test point in their correspondence. “N” Sectio Section n N consist consistss of “SOLDE “SOLDER R LESS LESS BREADB BREADBOAR OARD D OR PROTO PROTO BOARD” BOARD” It is consisting of so many holes.



Exp # 2.

VERIFICATION OF TRUTH TABLE OF BASIC LOGIC GATES Apparatus: 7408IC’s, Logic Trainer and connecting wires. OBJECTIVE The basic logic gates are the basic building blocks of more complex logic circuits. The purpose of this lab is to learn about Digital Logic and digital logic circuits. By the end of this lab you will have an understanding u nderstanding of the functions and operations of different logic gates. THEORY AND Gate The AND function is similar to the multiplication in mathematics. This is the all or nothing operator and it provides a logic 1 output only when all the inputs of the gate are at logic 1, and logic 0 output for all other input combinations. The AND function is described in terms of the following “truth table”. Figure 2 input AND Gate.

A 0 0 1 1

Truth Table of AND Gates i/p’s o/p B G1 G2 G3 0 1 0 1

G4

Comments: _____________________________________

________________________________________________ ________________________________________________



Exp # 3. VERIFICATION OF TRUTH TABLE OF BASIC LOGIC GATES Apparatus: 7432 ,7404,7402 IC’s, Logic Trainer and connecting wires. OBJECTIVE The basic logic gates are the basic building blocks of more complex logic circuits. The purpose of this lab is to learn about Digital Logic and digital logic circuits. By the end of this lab you will have an understanding u nderstanding of the functions and operations of o f different logic gates.

OR Gate The OR function is similar to the mathematical function of addition and the output for the OR gate may be analyzed using the laws of addition. The logic operator for the OR function is a + sign. The output will be logic 0 only if all the inputs are logic 0, and the output will be logic 1 anytime any input is at logic 1. Here, OUT = A +B. Figure 2 input OR Gate.

A 0 0 1 1

1

Truth Table of OR Gates i/p’s o/p B G1 G2 G3 0 1 0 1

G4

1

Comments: ______________________________________

_________________________________________________ _________________________________________________

NOT Gate The NOT circuit circuit or inverter performs performs the basic basic logic function function of complementation complementation.. It may be identified by the presence of a bubble on the input or the output of the traditional logic symbol. The output of NOT gate is the inverse of the input. Unlike the others it only has one input and one output. Figure 1 input NOT Gate -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 4

0 0 0 1


Truth Table of NOT Gates. i/p’s A 0 1

o/p G1

G2

G3

G4

Comments: ___________________________________

_____________________________________________ _____________________________________________

NAND Gate The NAND function is the complement of o f the AND function and the logic symbols have the inversion on the output. NAND gate is constructed by adding an inverter after AND operator. The NAND function provides logic 0 on the output only when both inputs are logic 1, and logic 1 output for all other combinations. Here, OUT = B A. Figure: 2-input NAND gate

Truth Table of NAND Gates i/p’s A 0 0 1 1

o/p B 0 1 0 1

G1

G2

G3

G4

Comments: _____________________________________

_______________________________________________ _______________________________________________

NOR Gate The complement of the OR function is the NOR function and the logic symbol has the inversion present on the output. NOR gate is constructed by adding an inverter after OR operator. Here, OUT = B A + . Figure: 2-input NOR gate



A 0 0 1 1

Truth Table of NOR Gates i/p’s o/p B G1 G2 G3 0 1 0 1

G4

Comments: __________________________________

____________________________________________ ____________________________________________

PROCEDURE • Place the IC 7408LS on the trainer board. • Connect VCC and ground to the respective pins on the trainer board. • Connect the inputs to the input switches provided in the trainer board. • Connect the outputs to the switches of output LEDs. • Apply various combinations of inputs as shown in the truth table and observe the • conditions of LEDs. • Similarly follow these steps for other gates. PROBLEMS • Measure the output voltages in all cases. • What is the difference between a Inverter and a NOT gate?

Lab Exercise:

1. Students are required to verify the functioning of each gate in each of there IC’s through T.Ts. 2. Then the gate, which is not functioning properly, should be clearly indicated.

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Exp # 4

IMPLEMENTATION OF MULTIVARIABLE BOOLEAN EXPRESSION USING LOGIC GATES. Apparatus: 7408, 7432, 7404 IC’s, logic kit and connecting wires. OBJECTIVE Boolean algebra uses many of the same laws as those of ordinary algebra. In this experiment, we’ll know about this laws & theorem. THEORY Generally you’ll find that the basic logic functions AND, OR, NAND, NOR, and NOT are not sufficient to implement complex digital logic functions. These gates are the basis for building more complex logic circuits that are constructed using various combinations of gates which is known as Combinational Logic. Combinational logic requires the use of two or more gates to form a useful, complex function. These complex functions usually begin as a Boolean Equation and the logic circuit may be implemented directly from this equation. The Boolean laws and rules are shown below:

Given Boolean function is

F1 = a b′ c + .a′ b c F2 = (a + b+ c′ ) (a′ + b)

a

b



Now we shall check the logic circuit by the following Truth Table. Truth Table o/p’s i/p’s A 0 0 0 0 1 1 1 1

B 0 0 1 1 0 0 1 1

F1 c 0 1 0 1 0 1 0 1

Actual

Observed

F2 Actual

Observed

Comments: _______________________________________________________

_________________________________________________________________ _________________________________________________________________ _________________________________________________________________

Lab Exercise: 1.

2.

Students are directed to write F1and F2 in terms of NAND and NOR gates only. Then implement F1 & F2 with universal gates and verify your result.

Comments: __________________________________________________________________________

____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________



Exp # 5.

VERIFICATION OF DEMORGAN’S THEOREM Apparatus: 7408, 7432, 7404 digital logic kit and connecting leads. OBJECTIVE De Morgan’stheorem allows for the simplification of a Boolean Expression by the cancellation of some redundant inversions. In this experiment, we’ll know about this laws & theorem. DE MORGAN`S THEOREM De Morgan developed a theorem that allows conversion between logic expressions that has inversions on the output to a different logic expression with the inversions on each of the inputs. This may allow for the simplification of a Boolean Expression by the cancellation of some redundant inversions. There are two Boolean Equations that represent De Morgan's Theorem:

It has two statements. 1. 2.

(x+y+z)′ = x′ .y′ .z′ where let F1 = (x+y+z)′ & F2 = x′ .y′ .z′ (x.y.z) ′ = x′ +y′ +z′ where let F3 = (x.y.z) ′ F4 = x′ +y′ +z′

x

y



Now we shall check this logic circuit by the Truth Table.

Truth Table i/p’s F1 = (x+y+z) x

y

z Actua l

0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1

o/p’s F2 = x .y .z F3 = (x.y.z)

Observ ed

Actu al

Observ ed

Actu al

Obser ved

F4 =x +y + z Actu Obser al ved

0 1 0 1 0 1 0 1

Comments: __________________________________________________________________________

____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________

PROCEDURE 1. At first construct the circuits shown in the Boolean laws. 2. Check if the laws are valid. Give truth tables for each law. 3. Construct the circuits shown in the circuit diagram. 4. Check if the two circuits give the same result. OBSERVATIONS & RESULTS 1. Write truth tables for each Boolean law. 2. Write the equation for the figure 1. Now try to simplify it and find the equation for figure 2 from it. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 10


Lab. Exercise: Students are directed 1. To write F1, F2, F3 and F4 in terms of NAND and NOR gates only. 2. Then implement F1, F2, F3 and F4 with Universal gates and verify your result. Comments: ________________________________________________________________________

___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________



Exp # 6.

TO REALIZE HALF & FULL ADDER USING BASIC LOGIC GATES. Apparatus: 7486, 7432, 7408, 7404 IC’s, logic kit and connecting leads. OBJECTIVE Digital computers perform a variety of information-processing tasks. Among the basic functions encountered are the various arithmetic operations. The most basic arithmetic operation is the addition of two binary digits. In this experiment we’ll know about the circuits that will add binary digits. THEORY Half Adder:

Half Adder is combinational logic circuit that generates the sum of two binary numbers (each having 1 bit length). The logic circuit has two inputs and two outputs i.e. Sum & Carry abbreviated as SHA & CHA respectively. First of all, we shall construct Truth Table of Half Adder Truth Table i/p’s

o/p’s

x

y

0 0 1 1

0 1 0 1

SHA = x y+xy Actual Observe d

CHA = x y Actua Observ l ed

Now we write Boolean function from above Truth Table as SHA =x′ y + xy′ CHA = xy Implementation

Now we implement above Boolean expression by basic logic gates i.e.



Now we shall check this logic circuit by the Truth Table of Half Adder.



Lab Exercise: 1. Students are required to write outputs of Full adder using Basic logic gates.. 2. Then implement Half Adder using basic logic gates. Full Adder:

Full Adder is combination logic circuit that performs the sum of 3 input binary numbers, (each having 1 bit length). Two of the binary input variables are x and y represent the two significant bits to be added the third input z, represents the carry from previous lower significant position. Outputs of Full Adder are Sum and Carry represented as SFA and CFA respectively. First of all, we shall construct Truth Table of Full Adder i.e. Truth Table i/p’s

o/p’s

x

y

z

0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1

SFA Actual Observ ed

CFA Actual Observ ed

Now we write Boolean expression for Sum and Carry of Full Adder. Sum = x′ y′ z+x′ yz′ +xy′ z′ +xyz Simplifying by using Boolean Postulates & theorems/k-map, we get Sum =(x′ y+xy′ ) ′ . z + (x′ y+xy′ ).z′ SFA = (x ⊕ y ) ⊕ z

Carry = x′ yz + xy′ z + xyz′ +xyz Simplifying by using Boolean Postulates & theorems/k-map, we get Carry = (x′ y+xy′ ) . z+xy CFA = (x ⊕ y) z + xy Implementation

Now we implement simplified Boolean expressions of SFA & CFA i.e.



x

y

SFA = (x y) z

CFA = (x We shall check this logic circuit by the Truth Table of Full Adder PROCEDURE • At first connect the circuit shown in the figure 1. • Vary the inputs as shown in the truth table. See if the circuit is true for all the combinations. • Now connect the circuit as shown in the figure 2. • Vary the inputs as shown in the truth table. See if the circuit gives us the result as shown in the table. OBSERVATIONS & RESULTS • Write the Boolean expressions for the figure 1 and find the sum and carry equation from those expressions (for half-adder). • Repeat step 1 for full- adder (figure 2). PROBLEM 1. Explain how the logic diagram of Figure 1 performs as a half adder. 2. Explain how the logic diagram of Figure 2 performs as a full adder. Lab Exercise:

1. 2.

Students are required to write outputs of Full Adder using Basic logic gates. Then implement output of Full Adder with Basic logic gates.


y) z + xy


Exp # 7. IMPLEMENTATION/DESIGN OF MAGNITUDE COMPARATORS Apparatus: 7486, 7432, 7408, 7404 logic kit and connecting wires. ONE BIT MAGNITUDE COMPARATOR

One Bit Magnitude Comparator is combination logic circuit which is used to compare two input binary numbers (each having one bit length) to check weather two inputs are equal or one less than other or greater then. First of all we write Truth Table of 1 Bit Magnitude Comparator i.e. Truth Table i/p’s x 0 0 1 1

y 0 1 0 1

E x=y 1 0 0 1

o/p’s G⇒x>y 0 0 1 0

L⇒x
Boolean functions for one bit Magnitude Comparator

E = xy+ x′y′ G = xy′ L = x′y Implementation

To check this logic circuit, we shall use the above Truth Table 2 BIT MAGNITUDE COMPARATOR

x

Two Bit Magnitude Comparator which is used to compare two input binary numbers (each having bit length of two ) to check weather two inputs are equal or one less than other or greater then.



USING XOR GATES AND BASIC LOGIC GATES First of all we write Truth Table of 2 Bit magnitude Comparator. Truth Table i/p’s A A1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

o/p’s B

A0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

B1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

B0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

E A=B 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

G⇒A>B 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0

L⇒A
Now we simplify outputs of 2 Bit Magnitude Comparator by k-map technique. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 17




k-map’s for outputs of 2 Bit Magnitude Comparator. k-map of “E”.

E k-map of “G”

k-map of “L”.

Boolean Functions

Now writing Boolean functions from above k-maps for outputs of two Bit Magnitude Comparator, we get. E = A′ 1 A′ 0 B′ 1 B′ 0+ A′ 1 A0 B′ 1 B0+ A1 A0 B1 B0+ A1 A′ 0 B1 B′ 0 E= A′ 1 B′ 1(A′ 0 B′ 0+ A0 B0) + A1 B1(A0 B0+ A′ 0 B′ 0) E = (A′ 0 B′ 0+ A0 B0) (A′ 1 B′ 1+ A1 B1) G = A1B′ 1+ A′ 1 A0 B′ 1 B′ 0+ A1 A0 B1 B′ 0 G = A1B′ 1 + A0 B′ 0 (A′ 1B′ 1+ A1 B1) L = A′ 1B1 + A′ 0 B0 (A′ 1B′ 1+ A1 B1) --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 19




Implementation

A

A

1 E

0

( = A0 +

0

) (B A1 +

G

L

= 1 B 1 +A

1

=1 B 1 + 'A

) B

0

BA ' 0 ( A1 +

'0 BA 0 ( ' A1 +

We check this circuit by Truth Table of 2 Bit Magnitude Comparator as written before.


1

) B'

1

) B'


Exp # 8.

DESIGN & IMPLEMENTATION OF A 2 x 4 DECODER Apparatus: 7432, 7408, 7404 IC’s logic kit and connecting leads Decoder : n 2n. n = No. of input lines. 2n = No. of outputs of a Decoder. Decoder is a circuit that convert binary information from n-input lines to max of 2 n output lines e.g. if we have 2 inputs i.e. x,y then there will be 4 output of a Decoder and size of Decoder will be 2X4.

Block Diagram of 2X4 Decoder.

s e n

Truth Table 2 X 4 Decoder

i/p’s x 0 0 1 1

y 0 1 0 1

Enable E 1 1 1 1

o/p’s d0 1 0 0 0

d1 0 1 0 0

d2 0 0 1 0

d3 0 0 0 1

Boolean Functions for 2 x 4 Decoder do = E x′ y′ d1 = E x′y d2 = E x y′ d3 = E x y



Implementation

x

Now we check this logic circuit by using Truth Tables of 2X4 Decoder as drawn above. Lab Exercise:

Students are directed to write the Truth Table of 3X8 Decoder with Enable. 2. Then, write output Boolean Functions of 3X8 Decoder. 3. Then implement 3X8 Decoder using logic gates. 1.



Exp # 9.

DESIGN OF A 2X1 and 4X1 MULTIPLEXER. Apparatus: 7432,7408,7404 logic kit and connecting wires Multiplexer Multiplexer, simply called Mux, is a data selector and is capable of “selecting” one of many input lines (usually 2n) and display its input status on the only output line available.

A Mux has 1. Select lines 2. Data input lines 3. Output line. Block diagram of 2x1 MUX

I0, I1 are inputs of Mux S is select line Y is output

The function table of 2x1 Mux is Select line S 0 1

o/p Y Io I1

The Boolean function for 2x1 Mux is Y = I1 s + I0 s



Logic Diagram of 2x1 Mux is

I1

s

Block diagram of 4x1 MUX

I0, I1,I2 and I3 are inputs of Mux S1 and S0 are select lines Y is output

The function table of 4x1 Mux is Select lines S1 S0 0 0 0 1 1 0 1 1

o/p Y Io I1 I2 I3

.

The Boolean function for 4x1 Mux is Y = I0 S1 S0 + S1 S0 I1+ S1 S0 I2+ S1 S0I3



Logic Diagram of 4x1 Mux is

We check this logic circuit by Function Table of 4X1 Mux as drawn above.



Exp # 10.

IMPLEMENTATION OF FULL ADDER USING MUX Apparatus: 74151 MUX, connecting wires. MUX : 2n 1. n = No. of select lines. 2n = No. of inputs of MUX if n = 3, size of MUX is 8x1 i.e.

Function Table x 0 0 0 0 1 1 1 1

Select lines y 0 0 1 1 0 0 1 1

z 0 1 0 1 0 1 0 1

o/p Y Io I1 I2 I3 I4 I5 I6 I7

Pin Configuration of 74151 MUX





Truth Table of Full Adder i/p’s of Full Adder x y z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

o/p’s S 0 1 1 0 1 0 0 1

C 0 0 0 1 0 1 1 1

Function Table of 8x1 Mux

i/p of Full Adder = Select lines of MUX x y z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

o/p of 8x1 mux S=Y 0 1 1 0 1 0 0 1

o/p of 8x1 mux C=Y 0 0 0 1 0 1 1 1

o/p of 8x1 mux

I0 I1 I2 I3 I4 I5 I6 I7

Procedure:

First of all we check/implement Carry of Full Adder (having 3 inputs) using 8X1 Mux, for this take : I0 = 0, I1 = 0, I2 = 0, I3 = 1, I4 = 0, I5 = 1, I6 = 1, I7 = 1, from Carry column of Truth table of Full Adder and then select x,y,z from Function table of 8X1 Mux and then observe outputs at Y Pin of 74151 IC, that should be equal to Carry of Full Adder for combination of x,y,z at select lines, which is inserted through data switches, this step is repeated for all x,y,z combinations, at select lines to observe Carry of Full Adder. Then we check/implement Sum of Full Adder for 3 input variables, using 8X1 Mux for this, we take : I0 = 0, I1 = 1, I2 = 1, I3 = 0, I4 = 1, I5 = 0, I6 = 0, I7 = 1, from Sum column of Truth Table of Full Adder, as data inputs to 8X1 Mux, and then for each combination of x,y,z at select lines from Function table. We see output at Y Pin of 74151 IC, which should be equal to value of Sum of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 29


Full Adder for x,y,z combination at select lines, which is inserted through data switches, this step is repeated for all x,y,z combinations, at select lines to observe Sum of Full Adder.



Exp # 11

IMPLEMENTATION OF FULL ADDER WITH 2, 2X4 DECODERS Apparatus: 74139, 7400 IC’s and connecting wires Decoder : n 2n. n = No. of input lines. 2n = No. of outputs of a Decoder. Decoder is a circuit that convert binary information from n-input lines to max of 2 n output lines e.g. if we have 2 inputs i.e. x,y then there will be 4 output of a Decoder and size of Decoder will be 2x4. Block Diagram of 2X4 Decoder.

s e n

Truth Table of 2X4 Decoder x 0 0 1 1

y 0 1 0 1

E 1 1 1 1

d0 1 0 0 0

d1 0 1 0 0

d2 0 0 1 0

d3 0 0 0 1

Boolean Functions for 2 x 4 Decoder

do = E x′ y′ d1 = E x′y d2 = E x y′ d3 = E x y Implementation



Now we implement Half Adder with 2x4 Decoder. Truth Table of Half Adder i/p’s x 0 0 1 1

o/p’s y 0 1 0 1

SHA 0 1 1 0

CHA 0 0 0 1

Truth Table of 2X4 Decoder i/p’s x 0 0 1 1

o/p’s y 0 1 0 1

d0 1 0 0 0

d1 0 1 0 0

d2 0 0 1 0

d3 0 0 0 1

By comparing Truth Tables of half Adder and 2 X 4 Decoder. We can see that

SHA = d1 + d2 CHA= d3

Block Diagram of Half Adder with Truth Table of 2X4 Decoder



Note: By connecting an OR gate with output Pin 1 & 2 of 2X4 Decoder. Half Adder can be implemented with 2X4 decoder. Similarly by connecting two Half Adders, we can form a Full Adder by using 2, 2X4 Decoder IC’s. Truth Table of Full Adder

x 0 0 0 0 1 1 1 1

i/p’s Y 0 0 1 1 0 0 1 1

o/p’s z 0 1 0 1 0 1 0 1

SHA 0 1 1 0 1 0 0 1

CHA 0 0 0 1 0 1 1 1

Block Diagram of Full Adder with 2, 2X4 Decoders.

Using the concept of implementation of Half Adder with 2X4 Decoder, we can implement Full Adder with 2, 2 X 4 Decoders.

Pin Configuration of 74LS139





EXP NO.12 VERIFICATION OF DIFFERENT TYPES OF FLIP FLOPS APPARATUS IC 7476, IC 7400,IC 7404 OBJECTIVE The aim of this experiment is to study the fundamentals of basic memory units and to become familiar with various types of flip-flops. We’ll verify the Truth tables of Flip-Flops: • RS-Type • D- Type • T- Type. • JK-Type THEORY RS flip-flop is also called Synchronous flip-flop. That means that this flip-flop is concerned with time. Digital circuits can have a concept of time using a clock signal. The clock signal simply goes from low-to-high and high-to-low in a short period of time .

Fig. 1 RS Flip Flop and its Truth Table In case of D flip-flop, The Q output always takes on the state of the D input at the moment of a rising clock edge. (or falling edge if the clock input is active low). It is called the D flip-flop for this reason, since the output takes the value of the D input or Data input, and Delays it by one clock count. The D flip-flop can be interpreted as a primitive memory cell, zero-order hold, or delay line.



In case of T flip-flop, if the T input is high, the T flip-flop changes state ("toggles") whenev er the clock input is strobed. If the T input is low, the flip-flop holds the previous value. The truth table is as follows:

The JK flip-flop augments the behavior of the SR flip-flop (J=Set, K=Reset) by interpreting the S = R = 1 condition as a "flip" or toggle command. Specifically, the combination J = 1, K = 0 is a command to set the flip-flop; the combination J = 0, K = 1 is a command to reset the flip-flop; and the combination J = K = 1 is a command to toggle the flip-flop, i.e., change its output to the logical complement of its current value. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 36


PROCEDURE • Make connections as shown in the diagrams. • Verify the truth tables for various combinations of inputs. PROBLEM • Draw a 1- to- 4 line multiplexer using basic gates. • Write the truth table for it.



LAB TEST (WEEK 13)



Exp No. 14

FAMILIARITY WITH VERILOG HDL Objectives:

A. Become familiar to Verilog environment. B. Use at least 2 levels of abstraction in your Verilog code. C. Write your own Verilog code in the lab D. Submit the lab report along with the answers of given questions. PreLab: This lab describes a hardware description language (HDL).A hardware description language is a language that describes hardware of a digital system, in a textual form. It can be used to represent logical diagrams, Boolean expressions and other complex digital circuits. The language contents can be stored and retrieved easily and can be processed by computer software in an efficient manner. Two major applications of this language are:

1. LOGICAL SIMULATION 2. SYNTHESIS Logical simulation It is the representation of the structure and behavior of a digital logical system through the use of a computer. The code that tests the functionalities of the design is called “Stimulus” or “Test Bench”. Synthesis Logical synthesis is the process of driving a list of components and their interconnections (called a NETLIST) from the module of a digital system in HDL. Levels of abstraction in Verilog

The level of abstraction to describe a module can be changes without any change in the environment there are four levels of abstraction: 

Behavioral Level



Dataflow Level



Gate Level



Switch Level



What is a Module? A module is the basic building block in Verilog. A module can b element of a collection of lower level design blocks. In Verilog, a module is declared by keyword module a corresponding end module must appear at the end of the module definition. Register Transfer Level Verilog allows the designer to mix and match all four levels of abstraction in a design. In the digital design community, the term register transfer level (RTL) is frequently used for a Verilog description that uses a combination of behavioral and data flow constructs and is acceptable to a logical synthesis tool.

Post Lab:

Answer 5 questions in this lab and submit then in your lab report. Lab Work: Verilog Code For simple two inputs AND Gate.

in p u t A Output in p u t B

Gate Level Verilog Code:

module and_gate (Out, A, B); //Starting of module and defining inputs and outputs input A, B; //inputs output Out; //outputs and A1(Out, A, B); //Gate level description of 2 inputs and 1 output AND gate endmodule module stim; //Stimulus module reg A,B; //Always make inputs as Reg or Registers wire Out; //Always make outputs as wire and_gate G1(Out, A, B); //Instantiation of main module (i.e. and_gate) initial begin A=0;B=0; #10 begin A=0;B=1;end #10 begin A=1;B=0; end #10 begin A=1;B=1; end --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 40


#10 begin A=1;B=1; end end endmodule

Truth Table For 2 Inputs AND Gate Input A Input B Output Out 0 0 0 0 1 0 1 0 0 1 1 1 Timing Diagram Verification for the written code:

• • • •

• •

• •

Some important things that we can see from the above code are: The module always start with keyword module Inside module () we define inputs and outputs but their sequence is not important But in case of gate level description it is very imp that output must be written before the inputs i.e. AND (Output, Input1, Input2 ……………...Input n) We can also define additional wires i.e. Links other than input or output as explained in the second example below Some keywords for gate level description are: A1(output(s), input1, input2, input3………………..input n)  and P1(output(s), input1, input2, input3………………..input n)  or N1(output(s), input1, input2, input3………………..input n)  not  nand D1(output(s), input1, input2, input3………………..input n) H1(output(s), input1, input2, input3………………..input n)  nor S1(output(s), input1, input2, input3………………..input n)  xor  xnor Q1(output(s), input1, input2, input3………………..input n) B1(output(s), input1, input2, input3………………..input n)  buf Stimulus module is used to verify the results that the code is working in a right fashion or not. At the end draw the truth table for the AND gate and verify your code according the output in the timing diagram and in the truth table



Dataflow Model Verilog Code:

module and_gate (Out, A, B); //Starting of module and defining inputs and outputs input A, B; //inputs output Out; //outputs //Data flow description of 2 inputs and 1 output AND gate assign Out=A&B; endmodule module stim; //Stimulus module reg A,B; //Always make inputs as Reg or Registers wire Out; //Always make outputs as wire and_gate G1(Out, A, B); //Instantiation of main module (i.e. and_gate) initial begin A=0;B=0; #10 begin A=0;B=1;end #10 begin A=1;B=0; end #10 begin A=1;B=1; end end endmodule The most important thing in data flow is the symbols that are used for different gates following are the symbols that are usually used for different gate Gate AND OR NOT XOR

Symbol Used & | ~ ^

Timing Diagram Verification for the written code:

Hence from the above timing diagram we can see that both out codes perform the same task the difference is of level of abstraction being used i.e. data flow or gate level Verilog code for a bit complex circuit. Used it as W IRE W i n v e r il o g c o d e A B

X

C

Y




module test(A,B,C,x,y); input A,B,C; output x,y; wire W; and A1(w,A,B); not N1(y,C); or S1(x,w,y); endmodule module stim; reg A,B,C; wire x,y; test TT(A,B,C,x,y); initial begin A=0;B=0;C=0; #10 begin A=0;B=0;C=1; end #10 begin A=0;B=1;C=0; end #10 begin A=0;B=1;C=1; end #10 begin A=1;B=0;C=0; end #10 begin A=1;B=0;C=1; end #10 begin A=1;B=1;C=0; end #10 begin A=1;B=1;C=1; end end endmodule Truth Table Input A 0 0 0 0 1 1 1 1

Truth Table for the given circuit Input B Input C Output y 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0

Output x 1 0 1 0 1 0 1 1



Timing Diagram Verification

Dataflow Model Verilog Code:

module test(A,B,C,x,y); input A,B,C; output x,y; wire W=A&B; assign y= ~ C; assign x=W | y; endmodule module stim; reg A,B,C; wire x,y; test TT(A,B,C,x,y); initial begin A=0;B=0;C=0; #10 begin A=0;B=0;C=1; end #10 begin A=0;B=1;C=0; end #10 begin A=0;B=1;C=1; end #10 begin A=1;B=0;C=0; end #10 begin A=1;B=0;C=1; end #10 begin A=1;B=1;C=0; end #10 begin A=1;B=1;C=1; end end endmodule



Lab Report Questions:

Q1: Write some properties of all four levels of abstraction described above (Hint: use internet for help)? Q2: Find all the keywords used in Verilog (Hint: use internet for help)? Q3: What is the difference between NET and REG in Verilog? Q4: Write Verilog code for the following code and also attach the timing diagrams and the truth table (Hint: Take help from your teacher)? A

B

X

Y

Z

L

M

N

O

P

Q5: Write Verilog code for the following code and also attach the timing diagrams and the truth table (Hint: Take help from your teacher)? A

B

O UT



Exp No. 15

UNDERSTATING BEHAVIORAL MODELING AND LEXICAL CONVENTIONS OF VERILOG HDL Objectives:

E. Understand the design methodologies. F. Lexical conventions. G. Data types being used in Verilog H. Develop code in Verilog using behavioral model I. Have some concept of gate delays J. Submit the lab report along with the answers of given questions.

PreLab:

Design Methodologies: There are two basic types of design methodologies: a top-down design methodology and a bottom-up design methodology. In a top down methodology, we define the top level block and identify the sub blocks necessary to build the top level block. We further subdivide the sub blocks until we come to leaf cells, which are the cells that cannot be further subdivided. The following figure shows the top-down design

T o p L e v e l B lo c k

S u b - B lo c k 1

L e a f C e ll

Sub-Block 2

L e a f C e ll

S u b - B lo c k 3

L e a f C e ll

L e a f C e ll

Figure: Top down design methodology

In a bottom up design methodology, we first identify the building blocks that are available to us. We build bigger cells, using these building blocks. These cells are then used for higher-level --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 46


blocks until we build the top level block in the design. Following figure shows the bottom-up design process T o p L e v e l B lo c k

m a c r o c e ll 1

m acro cell 1

L e a f C e ll

L e a f C e ll

m a c ro c e ll 1

L e a f C e ll

L e a f C e ll

Figure: Bottom-up design methodology

Lexical Conventions in Verilog

•

White Spaces: Blank space (\b), tabs (\t), and new lines (\n) comprise the white spaces. White space is ignored by the Verilog except when it separates tokens. White space is not ignored in strings •

Comments: Comments can be inserted into the code for readability and documentation. There are two ways to write comments. A one line comment starts with “//”. Verilog skips from that position to the end of the line. A multiple comment starts with “/*” and ends with “*/”.

a = b && c; //This is a one line comment /* This is a multiple line Comment*/ /* This is /* an illegal */ comment */ /* This is // a legal comment */

•

Operators:



Operators are of three types: unary, binary and ternary. Unary operators precede the operands. Binary operators appear between two operands. Ternary operators have two separate operators that separate three operands

a = ~ b; // ~ is a unary operator a = b && c; // && is a binary operator a = b? c : d; // ?: is a ternary operator

•

Number Specification: 

Sized Numbers Sizes numbers are represented as ’. is written only in decimal and specifies the number of bits in the number. Legal base formats are decimal (d or D), hexadecimal (h or H), binary (b or B) and octal (o or O). the number is specifies as consecutive digits from 0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f. only a subset of these digits is legal for a particular base.

4’b1111 12’habc 16’d255

//This is a 4-bit binary number //This is a 12-bit hexadecimal number //This is a 16-bit decimal number



Unsized Numbers Numbers that are specifies without a specification are decimal numbers by default. Number that are written without specification hav e a default no of bits that is simulator or machine specific (must be at least 32)

23456 ‘hc3 ‘o21

//This is 32-bit decimal number by default //This is a 32-bit hexadecimal number //This is a 32-bit octal number



X or Z values Verilog has two symbols for unknown and high impedance values. These values are very important for modeling real circuits. An unknown value is denoted by an x. A high impedance value is denoted by z.



12’h13x 6’hx 32’bz

//This is a 32-bit hex number 4 least significant bits unknown //This is a 16-bit hex number //This is a 32-bit high impedance number

•

Strings: A string is a sequence of characters that are enclosed by double quotes. The restriction on a string is that is must contain on a single line, that is without carriage return. it cannot be on multiple lines

“Hello Verilog World” “a / b”

//is a string //is a string



Gate Delays in Verilog In Verilog the date delays is generally represented by # symbol along with the gate function

Post Lab: Answer all questions in this lab and submit then in your lab report. Lab Work: Simple circuit with delays A B

X

30ns 20ns

C

Y 10ns

Verilog Code:

module test(A,B,C,x,y); input A,B,C; output x,y; wire W; and #30 not #10 or #20 endmodule

Gate Delay of 10n Seconds

A1(w,A,B); N1(y,C); S1(x,w,y);

module stim; reg A,B,C; wire x,y; test TT(A,B,C,x,y); initial begin A=0;B=0;C=0; #10 begin A=0;B=0;C=1; end #10 begin A=0;B=1;C=0; end --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 50


#10 begin A=0;B=1;C=1; end #10 begin A=1;B=0;C=0; end #10 begin A=1;B=0;C=1; end #10 begin A=1;B=1;C=0; end #10 begin A=1;B=1;C=1; end #100 $finish; end endmodule

Timing Diagram Verification for the written code:

Verilog code for half adder. Y

X

Sum

Carray


module test(x,y,Sum,Carry); input x,y; output Sum,Carry; xor A1(Sum,x,y); and N1(Carry,x,y); endmodule module stim; reg x,y; wire Sum,Carry; --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 51


test TT(x,y,Sum,Carry); initial begin x=0;y=0; #10 begin x=0;y=1; end #10 begin x=1;y=0; end #10 begin x=1;y=1; end #10 $finish; end endmodule Timing Diagram Verification


Q1: Write all System tasks and compiler directives along with their functions performed like $  $display, $monitor, $time, $stop, $finish etc (Hint: use internet for help)? Q2: Explain the syntax and usage of Integer, Real, Time Register data types used in Verilog. Also explain the syntax and usage of Arrays and Vectors (Hint: use internet for help)? Q3: Write the difference between INITIAL block and ALWAYS block used in Verilog and also explain the difference between TASKS and FUNCTIONS used in Verilog? Q4: Explain the usage of FOLK and JOIN statements in Verilog with the help of example? Q5: Write Verilog code (in behavior model) for the following diagram and also attach the timing diagram and the truth table (Hint: Take help from your teacher)?



Full A dd er X Y

Sum

Z Carray

Q6: Write Verilog code (in behavior model) for the following diagram and also attach the timing diagram and the truth table (Hint: Take help from your teacher)?

4 - B i t F u ll A d d e r B[3]

A [3 ]

FA3

B [2 ]

C 3

B [1 ]

A [2 ]

FA 2

C 2

A [1 ]

FA 1

B [0 ]

C 1

A [0 ]

FA 0

C in

Cout

S [3 ]

S [2 ]

S[1]

S[0]



Exp No. 16

WRITING MORE CODES IN VERILOG HDL AND UNDERSTANDING THE GATE DELAYS

Objectives:

K. Understand some of the Verilog basic concepts. L. Understand the module structure in Verilog. M. Understanding port connection rules used in Verilog. N. Defining gate delay types. O. Submit the lab report along with the answers of given questions. Modules:

A module in Verilog consists of the following parts: Module Name, Port List, Port Declaration (if ports present) Parameters (optional)

Declaration of wires, regs and other variables

Data flow statements (Assign)

Instantiation of lower Level modules

Always and initial blocks. All behavioral statements Go in these blocks.

Tasks and Functions

endmodule statement Components of a Verilog module



Port Connection Rules: One can visualize a port as consisting of two units. One unit that is internal to the module and another that is external to the module. The internal and external units are connected. There are rules governing ports connections when modules are instantiated within other modules. The Verilog simulator complains if any port connection rules are violated. These rules are simulated in the following figure:

net

net

input net reg or net

in o u t

output reg or net

net

Port Connection Rule 

Inputs: Internally, input ports must be of the type net . Externally, the inputs can be connected to a variable which is a reg or a net. 

Outputs: Internally, output ports can be of type reg or net . Externally, outputs must always be connected to a net. They cannot be connected to a reg. 

Inouts: Internally, inout ports must always be of type net . Externally inout ports must always be connected to a net . 

Width matching: It is illegal to connect internal and external items of different items of different sizes when making intermodule port connections. However, a warning is typically issued that the widths do not match.  Unconnected Ports: Verilog allows ports to remain unconnected. For example, certain ports might be simply for debugging, and you might not be interested in connecting them to the external signals



Gate Delays in Verilog: There are three types of delays in Verilog HDL i.e. Rise, Turn off and Fall delays •

Rise delay: The rise delay is associated with a gate output transition to a 1 from another value

1

0 , x o r z

t_rise

•

Fall delay: The fall delay is associated with a gate output transition to a 0 from another value 1 , x o r z

0

t_fall

•

Turn-off delay: The turn off delay is associated with a gate output transition to the high impedance value (x) from another value. If the value changes to x, the minimum of the three delays is considered Post Lab:

Answer all questions in this lab and submit them in your lab report.



Lab Work:

Create the Verilog code of the following diagrams in the lab. (Using any model, but most preferably BEHAVIOURAL MODEL) 1) A

output

A >B

output

A
input

4-bit C o m p a ra to r B

input

A==B

output

2) S2

S1

n o i t c e l e S

A

input

B

input

C

input

D

input

n o i t c e l e S

X 1 U X M 4

output

O UT

3) D Q

CLK

D-LATCH

Q

(not)


Q1: Explain the difference between continuous assignment and implicit continuous assignment with the help of an example in data flow models? --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Digital System Lab,CPED, UET Taxila 57

Labs_Digital Logic Design Manual

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