JURUSAN ILMU KOMPUTER
Modul Praktikum SISTEM DIGITAL Oleh : Tim Praktikum SISTEM DIGITAL TEKNIK INFORMATIKA 2011/2012
Modul Praktikum Sistem digital ini digunakan sebagai acuan pelaksanaan Praktikum Sistem Digital di Lingkungan Jurusan Ilmu Komputer – Fakultas Matematika dan Ilmu pengatahuan Alam, Universitas Udayana.
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TATA TERTIB PRAKTIKUM SISTEM DIGITAL SEMESTER GENAP TAHUN AJARAN 2011/2012
1. Pengerjaan Praktikum adalah 14 hari setelah soal dikeluarkan. 2. Demo praktikum akan dilaksanakan pada akhir minggu ke-2 sejak soal dikeluarkan (hari ke-14). 3. Terdapat 2 jenis tugas tugas dalam tiap Modul Modul yaitu a. Tugas Pendahuluan
Tugas Pendahuluan wajib diresponsi oleh setiap kelompok maksimal 1 minggu setelah soal dikeluarkan.
Tugas pendahuluan yang sudah benar, akan di acc.
Apabila responsi tugas pendahuluan melampaui batas waktu, maka tugas pendahuluan tidak akan di acc.
Tugas pendahuluan di responsi dalam bentuk hard copy
b. Tugas Modul
Tugas Modul baru bisa dikerjakan apabila tugas pendahuluan sudah di acc.
Tugas Modul wajib diresponsi maksimal H-1 demo praktikum (hari ke-13).
Tugas modul di responsi dalam bentuk hard copy
4. Urutan demo praktikum akan diacak saat pelaksanaan demo praktikum. 5. Apabila kelompok yang mendapat giliran tidak bisa melaksanakan demo, maka
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7. Penilaian praktikum adalah a. Nilai Tugas Pendahuluan (30%) i. Kelompok 1. Responsi (20%) 2. Tugas pendahuluan (5%) ii. Perseorangan (5%)
b. Nilai Tugas Modul (70%) i. Kelompok 1. Demo (40%) 2. Laporan akhir (20%) ii. Perseorangan (10%) 8. Setiap kelompok praktikum wajib mentaati semua aturan yang berlaku di Ilkom UNUD
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Teknik Informatika – Universitas Udayana
MODUL I
ALJABAR (ALJABAR BOOLEAN BOOLEAN) Agus Muliantara, S.Kom, M.Kom
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1 A ljabar B oolean
MODUL I ALJABAR BOOLEAN
Tujuan Praktikum :
1. Mengenalkan fungsi logika 2. Menganalkan prinsip-prinsip Aljabar Boolean 3. Mengenalkan fungsi kanonik.
Indikator Pencapaian :
Praktikan mampu memahami prinsip-prinsip yang berlaku pada aljabar logika Boolean.
Materi : Aljabar Boolean
Matematika Merupakan sarana yang berguna dalam analisis rangkaian logika digital. Semua operasi logika dalam suatu rangkaian logika tergantung pada ada atau tiadanya sisnyal, suatu variabel logika hanya dapat memiliki satu dari dua nilai yang mungkin terjadi yaitu 0 atau 1. Matematika dengan dua nilai itu disebut dengan Aljabar Boolean dua nilai. Aljabar Boolean dapat didefinisikan dengan suatu himpunan unsur dan sejumlah aturan-aturan aturan-aturan untuk menentukan logika digital, atau “switching algebra”, algebra”, yaitu berupa aksioma-aksioma dan teorema-teorema. Operator-operator yang digunakan pada Aljabar Boolean : { · , + , „ , membantu
atau
}.
Aksioma-aksioma dan Teorema-aksioma digunakan untuk
mereduksi
logika
kompleks
menjadi
meningkatkan “area dan kecepatan” dari rangkaian digital. digital.
Ak sioma d dan T Teorema p pada A Al j Boolean jabar B
logika
lebih
sederhana-
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2 A ljabar B oolean
Ber ik ut A Ak sioma-ak sioma d dan tteor ema-teor ema d dalam A Al ja j bar B ja ba Boolean :: (A1) X = 0 if X ≠ 1 (A1’) X = 1 if X ≠ 0 (A2) If X = 0, then X’ = 1 (A2’) if X = 1, then, then, X’ = 0 (A3) 0 . 0 = 0 (A3’) 1 + 1 = 1 (A4) 1 . 1 = 1 (A4’) 0 + 0 = 0 (A5) 0 . 1 = 1 . 0 = 0 (A5’) 1 + 0 = 0 + 1 = 1 (T1) X + 0 = X (T1’) X . 1 = X X (T2) X + 1 = 1 (T2’) X . 0 = 0 (T3) X + X = X (T3’) X . X = X X (T4) (X’)’ = X X (T5) X + X’ = 1 (T5’) X . X’ = 0 0 (T6) X + Y = Y + X (T6’) X . Y = Y . X (T7) (X + Y) + Z = X + (Y + Z) (T7’) (X . Y) . Z = X . (Y . Z) (T8) X . Y + X . Z = X . (Y + Z) (T8’) (X + Y) . (X + Z) = X + Y . Z (T9) X + X . Y = X (T9’) X . (X + Y) = X (T10) X . Y + X . Y’ = X (T10’) (X + Y) . (X + Y’) = X (T11) X . Y + X’. Z + Y . Z = X . Y + X’ . Z (T11’) (X + Y) . ( X’ + Z) . (Y + Z) = (X + Y) . (X’ + Z) (T12) X + X + . . . + X = X (T12’) X . X . . . . . X = X
(Identities) (Null elements) (Idempotency) (Involution) (Complements) (Commutativity) (Associativity) (Distributivity) (Covering) (Combining) (Consensus) (Generalized idempotency)
(T13) (X . X . . . . . X )’ = X ’ + X ’ + . . . + X ’ 1
2
n
1
2
n
(T13’) (X + X + . . . + X )’ = X ’ . X ’ . . . . . X ’
(DeMorgan’s theorems)
(T14) [F(X , X , . . ., X , +, .)]’ .)]’ = F(X ’, X ’, . . ., X ’, . , +)
(Generalized DeMorgran’s theorem)
1
2
1
2
n
1
n
2
1
n
2
n
Contoh m mani p ek s pr esi B Boolean pulasi e Bagaimana m menyatak an ((A ·· B B + + C C)? Gunak an tteor ema D DeMor gan.
A ·· B B + + C C
= (( (( A A ·· B B + + C C ))‟ ))‟
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3 A ljabar B oolean
Ter m pen jumlahan:
Ek s pr pr esi sum-of - pr pr oducts ((SOP):
Z‟ + + ((W ·· X X ·· Y Y) + + ((X ·· Y Y‟ ·· Z Z) + + ((W‟ ·· Y Y‟ ·· Z Z)
Ek s pr pr esi pr ppr oduct-of -sums ((POS) ::
Z‟, ((W + + X X + + Y Y), ((X + + Y Y‟ + + Z Z), ((W‟ + + Y Y‟ + + Z Z)
Z‟ ·· ((W + + X X + + Y Y) ·· ((X + + Y Y‟ + + Z Z) ·· ((W‟ + + Y Y‟ + + Z Z)
Ter m n nor mal: tter m pe per k atau pe pen ju jumlahan d di d dalamnya ttidak a var ia be bel y yang ka lian a ada v muncul lle bi bih d dar i ssek ali Contoh tter m-ter m n non-nor mal:
W·X·X·Y‟ W+W+X‟+Y
Contoh tter m-ter m n nor mal:
W·X·Y‟
W+X‟+Y
X·X‟·Y 0
Minterm d dan M Maxterm
Minterm:
Se bu buah m minter m n n-var ia be bel m mer u pa pak an sse bu buah tter m pe per k nor mal d dengan ka lian n liter als. n
Ter da pat 2 2n tter m per k yang d demik ian. ka lian y
Contoh m minter m 4 4 v var ia bel: W ·· X X‟ ·· Y Y‟ ·· Z Z‟
W ·· X X ·· Y Y‟ ·· Z Z
W‟ ·· X X‟ ·· Y Y ·· Z Z‟
Da pa pat d didef inisik an sse ba bagai sse bu buah tter m pe per k yang = = 1 1 pa pada be benar - be benar ka lian y satu ba bar is d dar i tta be bel k k e be benar an
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4 A ljabar B oolean
Minterms/Maxterms u untuk S Fungsi 3 3 V Variabel Sebuah F
Representasi Penjumlahan Kanonis Minter m ii :: B Bar is ii d dar i tta bel k k e benar an y yang m memilik i k k eluar an 1 1.
Pen ju jumlahan K K anonis ((C anonical su s dar i sselur uh m minter ms u untuk sum): JJumlah d suatu f f ungsi y yang d di be b pada ((ta be bel k k e be benar an). ber ik an pa
Notasi u untuk F Minter m a adalah :: ∑ Fungsi M Contoh: ∑ X,Y,Z ((0, 3 3, 4 4, 6 6, 7 7) = X‟·Y‟·Z‟ + X‟·Y·Z + + X X·Y‟·Z‟ + + X X·Y·Z‟ + + X X·Y·Z
R e pr esentasi ini bbiasa dir ealisasi dengan menggunak an r angk aian logik a A ND ND-OR 2 level dengan inver ter -inver ter pa p ba bang pada masuk an-masuk an ger A ND, sse per ti y yang d di p per luk an. Contoh pe pen ju jumlahan k k anonis
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5 A ljabar B oolean
F = ∑ X,Y,Z ((0, 3 3, 4 4, 6 6, 7 7) = X‟·Y‟·Z‟ + + X X‟·Y·Z + + X X·Y‟·Z‟ + + X X·Y·Z‟ + + X X·Y·Z R epresentasi p perk alian k k anonis
Maxter m ii: bar is ii d dar i tta bel k k e benar a y yang m mem punyai k k eluar an 0 0
Pek alian k anonis: Per k untuk s di be b ka lian dar i maxter ms u suatu f ungsi yang d ber ik an pa pada ((ta be bel k k e be benar an)
Notasi π :: Contoh: π X,Y,Z ((1,2,5) = ((X + + Y Y + + Z Z‟) .. ((X + + Y Y‟ + + Z Z) .. ((X‟ + + Y Y + + Z Z‟)
R e pr pr esentasi d dir ealisasi d dengan m menggunak an r r angk aian logik a O OR -A ND ND 2 2 level d dengan iinver ter p masuk an-masuk an g ger bang O OR , sse per ti d di b pada m butuhk an Contoh per k k anonis ka lian k Fungsi d dir e pr pr esentasi d dengan tta be bel k k e be benar an: Row 0 1 2 3 4 5 6 7
X 0 0 0 0 1 1 1 1
Y 0 0 1 1 0 0 1 1
Z 0 1 0 1 0 1 0 1
F 1 0 0 1 1 0 1 1
Memilik i r r e pr pr esentasi pe per k k anonis S Se ba bagai be ber ik ut: ka lian k
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6 A ljabar B oolean
I.
Tugas Pendahuluan 1. Sederhanakanlah fungsi-fungsi berikut, jelaskan teorema dan aksioma yang digunakan!
a. x’y’+xy+x’y b. abc + ac + bc c. (x+y).(x+y’) d. ( x’y + y’ x )’ + x y e. abd + a’b’d + abd’ 2. apa yang dimaksud dengan bentuk perkalian kanonis dan bentuk penjumlahan kanonis? kanonis? II.
Tugas Modul : A. Kelompok Ganjil :
1. Dengan Menggunakan Tabel kebenaran, buktikan kebenaran teorema aljabar berikut : a. DeMorgan untuk tiga variabel. b. Hukum Distributif • dan +. 2. Sederhanakan fungsi berikut ini menjadi bentuk yang paling sederhana dengan teorema-teorema dan aksioma-aksioma yang ada (tuliskan teorema/aksioma yang digunakan) :
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7 A ljabar B oolean
A1 = z = z + wxy +w’y B1 = (wx)’ + w’x’ + y’z + w’yz’ 4. Nyatakan Fungsi-fungsi Boole berikut : a. F = xy + xz’ ke ke dalam bentuk hasil kali kanonis (Maxterm) b. F = xy’ + z ke dalam bentuk penjumlahan kanonis (Minterm) B. Kelompok Genap :
1. Dengan Menggunakan Tabel kebenaran, buktikan kebenaran teorema aljabar berikut : c. DeMorgan untuk tiga variabel. d. Hukum Distributif • dan +. 2. Sederhanakan fungsi berikut ini menjadi bentuk yang paling sederhana dengan teorema-teorema dan aksioma-aksioma yang ada (tuliskan teorema/aksioma yang digunakan) :
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8 A ljabar B oolean
III.
Laporan Laporan diketik rapih pada kertas A4 dan dikumpulkan pada waktu yang telah
ditentukan. Format Penulisan Laporan :
Font Tulisan
: Times New Roman 12 pt
Font Source Code
: Courier New 10 pt
Line Spacing
: Single
Margin
: 4, 3, 3, 3 (left, top, right, bottom)
Isi Laporan
: BAB I LANDASAN TEORI BAB II PERMASALAHAN BAB III PEMBAHASAN
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TATA TERTIB PRAKTIKUM SISTEM DIGITAL SEMESTER GENAP TAHUN AJARAN 2011/2012
1. Pengerjaan Praktikum adalah 14 hari setelah soal dikeluarkan. 2. Demo praktikum akan dilaksanakan pada akhir minggu ke-2 sejak soal dikeluarkan (hari ke-14). 3. Terdapat 2 jenis tugas tugas dalam tiap Modul Modul yaitu a. Tugas Pendahuluan Tugas Pendahuluan wajib diresponsi oleh setiap kelompok maksimal 1
minggu setelah soal dikeluarkan. Tugas pendahuluan yang sudah benar, akan di acc. Apabila responsi tugas pendahuluan melampaui batas waktu, maka tugas
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7. Penilaian praktikum adalah a. Nilai Tugas Pendahuluan (30%) i. Kelompok 1. Responsi (20%) 2. Tugas pendahuluan (5%) ii. Perseorangan (5%)
b. Nilai Tugas Modul (70%) i. Kelompok 1. Demo (40%) 2. Laporan akhir (20%) ii. Perseorangan (10%) 8. Setiap kelompok praktikum wajib mentaati semua aturan yang berlaku di Ilkom -
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Teknik Informatika | Universitas Udayana
MODUL II
(GERBANG LOGIKA)
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1
G erba erbang L ogi ka
MODUL II Gerbang Logika Tujuan Praktikum :
1. Mengenalkan dasar-dasar dari gerbang logika. 2. Mengenalkan cara perancangan logika sederhana. 3. Mengenalkan implementasi gerbang dasar dan universal.
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2
G erba erbang L ogi ka Berikut adalah bentuk dari penjumlahan, perkalian dan negasi logis :
Penjumlahan Logis (OR)
Perkalian Logis (AND)
Negasi (NOT)
0+0=0
0.0=0
0=1
0+1=1
0.1=0
1=0
1+0=1
1.0=0
1+1=1
1.1=1
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3
G erba erbang L ogi ka adalah tanda titik (.). Gerbang AND mempunyai beberapa input dan satu output.
Lambang :
Fungsi :
Y = A.B Y = A.B.C
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4
G erba erbang L ogi ka Tabel Kebenaran OR : Tabel kebenaran untuk dua input.
Tabel kebenaran untuk dua input
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5
G erba erbang L ogi ka Tabel Kebenaran : Tabel kebenaran untuk dua input.
Tabel kebenaran untuk dua input
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6
G erba erbang L ogi ka Selain kedua jenis gerbang tersebut terdapat pula gerbang kombinasi yang terbentuk dari kombinasi tiga gerbang dasar yaitu AND, OR dan NOT. Gerbang Tersebut
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7
G erba erbang L ogi ka Tabel Kebenaran XNOR
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8
G erba erbang L ogi ka 3. Gerbang logika dapat dicari pada menu navigasi navigasi Devices Devices Hotkeys2. Hotkeys2. Pilihlah device sesuai dengan kebutuhan.
Hotkeys1 atau Hotkeys1 atau
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G erba erbang L ogi ka 3. Untuk fungsi Boole x’y’z +x’ F = x’y’z +x’ yz +yz
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G erba erbang L ogi ka Laporan
Laporan diketik rapih pada kertas A4 dan dikumpulkan pada waktu yang telah
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9
R ang kaian kaian S ekuensi al
Counter
Counter merupakan sekelompok flip-flop yang disusun sedemikian rupa yang mampu melakukan pencacahan output dengan sinkronisasi dari clock. State Diagram
Jenis-jenis angka pada counter :
Pencacah modulo 4
Pencacah modulo 8
Pencacah modulo 10 dst.
Macam-macam C Counter
Up Counter
Menghitung / mencacah mencacah input dari pulsa dari yang terendah
menuju yang tertinggi sampai batas yang ditentukan.
Down Counter
Adalah kebalikan dari up counter yakni menghitung atau
mencacah bilangan angka tinggi menuju bilangan rendah.
Up-Down Counter kombinasi dari up conter dan down counter
Dalam pembuatan counter hal penting yang harus diperhatikan adalah
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10
R ang kaian kaian S ekuensi al (counter-up modulo 8), kita dapat menentukan perjalanan output-ouput yang dihasilkan yaitu mulai dari 000001010011100101110111000. Berikut contoh dari rangkaian Up-Down Counter modulo 5 dengan flip-flop flip-flop JK :
S J CP K
5V
Q _ Q R
S J CP K
S Q _ Q
R
J CP K
Q _ Q R
5V
R ef erensi ::
1. Mano, M. and Prentice Hall. 2002. Digital 2002. Digital Design. Design. New Jersey. 2. Mismail, Budiono. 1998. Dasar-Dasar 1998. Dasar-Dasar Rangkaian Logika Digital . Bandung : ITB
Soal Pendahuluan
1. Implementasikanlah rangkaian SISO, SIPO, PISO, PIPO dan Bidirectional Shift Registers pada software simulasi rangkaian digital circuit maker dengan empat buah flip-flop atau memori penyimpanan!
Pelaksanaan Praktikum
1. Tools Praktikum
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11
R ang kaian kaian S ekuensi al 2. Praktikum Untuk mengerjakan soal pendahuluan yang ada diatas, adapun langkahlangkah yang harus dilaksanakan adalah : 1. Bukalah aplikasi circuit maker 5.0 pada computer masing-masing. 2. Untuk menggunakan rangkaian flip-flop, klik Devices
Browse, Browse,
maka akan muncul sebuah jendela baru yaitu jendela Device jendela Device Selection. Selection. 3. Pilih Digital basics pada Mayor Device Class dan pilih Flip-flops pada Minor Device Class Class dan tentukanlah flip-flop yang anda ingin gunakan pada Device pada Device symbol . 4. Setelah menentukan flip-flop yang digunakan, langkah selanjutnya adalah menyusun rangkaian sesuai dengan konsep dan teori dasar. 5. Setelah berhasil menyusun lalu lakukan simulasi rangkaian dengan klik
6. Semua rangkaian dapat dibuat dalam satu worksheet dengan dengan kata lain dapat diuji secara bersama-sama dan tidak perlu membuat banyak worksheet circuit maker . Soal Modul A. Kelompok Ganjil :
1. Jelaskan secara detail konsep istilah-istilah berikut ini : a. Flip-flop. b. Register Geser. c. SISO (sertakan contoh implementasi). d. PISO (sertakan contoh implementasi). e. Bidirectional Shift Registers (sertakan contoh implementasi). f. Ring Counter.
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12
R ang kaian kaian S ekuensi al 2. Buatlah rangkaian counter up-down modulo 11 dengan menggunakan flip-flop JK, rangkaian memiliki karakteristik counter up untuk bilangan ganjil dan counter down untuk bilangan genap! 3. Sebuah hotel yang berlantai 15 direncanakan akan dibuatkan lift. Layaknya sebuah lift, lift itu bisa naik dan turun . Akan tetapi, lift ini dilengkapi dengan pemercepat, jika pemercepat bernilai 0, maka lift akan bergerak 1 lantai per-detik (per-hentakan), jika pemercepat bernilai 1, maka lift akan bergerak 3 lantai perdetik. buatlah simulasinya dengan flip-flop D.
Catatan :
1. Untuk soal nomor 2 dan 3 jawaban soal tidak hanya berupa rangkaian saja, melainkan juga menyertakan analisis dan dokumentasi perancangan rangkaian. 2. Persiapkan file softcopy rangkaian (.ckt) untuk keperluan demo.
B. Kelompok Genap :
1. Jelaskan secara detail konsep istilah-istilah berikut ini : a. Flip-flop. b. Register Geser. c. SISO (sertakan contoh implementasi). d. PISO (sertakan contoh implementasi). e. Bidirectional Shift Registers (sertakan contoh implementasi). f. Ring Counter. g. Ripple Counter.
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13
R ang kaian kaian S ekuensi al 2. Buatlah rangkaian counter up-down modulo 16 dengan menggunakan flip-flop JK, rangkaian memiliki karakteristik counter up untuk bilangan genap dan counter down untuk bilangan ganjil! 3. Sebuah hotel yang berlantai 10 direncanakan akan dibuatkan lift. Layaknya sebuah lift, lift itu bisa naik dan turun . Akan tetapi, lift ini dilengkapi dengan pemercepat, jika pemercepat bernilai 0, maka lift akan bergerak 1 lantai per-detik (per-hentakan), jika pemercepat bernilai 1, maka lift akan bergerak 2 lantai perdetik. buatlah simulasinya dengan flip-flop D.
Catatan :
1. Untuk soal nomor 2 dan 3 jawaban soal tidak hanya berupa rangkaian saja, melainkan juga menyertakan analisis dan dokumentasi perancangan rangkaian. 2. Persiapkan file softcopy rangkaian (.ckt) untuk keperluan demo.
Laporan
Laporan diketik rapih pada kertas A4 dan dikumpulkan pada waktu yang telah ditentukan. Format Penulisan Laporan :
Font Tulisan
: Times New Roman 12 pt
Font Source Code
: Courier New 10 pt
Line Spacing
: Single
Margin
: 4, 3, 3, 3 (left, top, right, bottom)
Isi Laporan
: BAB I LANDASAN TEORI BAB II PERMASALAHAN