This document discusses logic gates and Boolean algebra. It contains the following key points: 1. Logic gates are circuits that have one or more inputs and produce a single output. Common logic gates include inverters, AND, OR, NAND, NOR, EXOR, and EXNOR gates. 2. Boolean algebra is used to design digital circuits. It has laws like commutativity, associativity, and distributivity. Boolean formulas are used to represent the functions of logic gates. 3. Truth tables are provided that define the output of each logic gate for all possible combinations of its inputs. Timing diagrams also graph the input and output signals over time.

1. GERBANG LOGIKA
ARIF LUKMAN HAKIM
13.04.51.0013

2. GERBANG LOGIKA
• Gerbang merupakan rangkaian dengan satu atau lebih
sinyal masukan, tetapi hanya menghasilkan satu sinyal
keluaran.
• Gerbang dinyatakan dengan dua keadaan :
▫ Tegangan tinggi / logika tinggi / high logic / logika 1
▫ Tegangan rendah / logika rendah / low logic / logika 0
• Rangkaian digital dirancang dengan menggunakan
Aljabar Boole, penemunya George Boole.

3. Gerbang Logika Dasar
Jenis
Gerbang
Simbol Grafis dan
Fungsi Aljabar
Tabel
Kebenaran
Timing Diagram
Inverter
(NOT)
AND
OR
Y = A
A Y
0 1
1 0
A B Y
0 0 0
0 1 0
1 0 0
1 1 1
Input Output
A Y
A
B
Y
A
B
Y
A B Y
0 0 0
0 1 1
1 0 1
1 1 1
Y = A . B
Y = A + B
A
B
Y
A
B
Y
Y
A

4. Gerbang Logika Lain
A B Y
0 0 1
0 1 1
1 0 1
1 1 0
Jenis
Gerbang
Simbol Grafis dan
Fungsi Aljabar
Tabel Kebenaran Timing Dagram
NAND
(NOT AND)
NOR
(NOT OR)
A
B
Y
A
B
Y
A B Y
0 0 1
0 1 0
1 0 0
1 1 0
Y = A + B
Y = A . B
A
B
Y
A
B
Y

5. Gerbang Logika Lain (Cont..)
A B Y
0 0 0
0 1 1
1 0 1
1 1 0
Jenis
Gerbang
Simbol Grafis dan
Fungsi Aljabar
Tabel Kebenaran Timing Diagram
EX-OR
EX-NOR
B
A
Y
BAY 
A B Y
0 0 1
0 1 0
1 0 0
1 1 1
A
B
Y
BAY 
A
B
Y
A
B
Y

6. Menurunkan Tabel Kebenaran
Contoh :
1. A
B
A
Y = A + B
A B A Y
0 0 1 1
0 1 1 1
1 0 0 0
1 1 0 1
2. A
B
C B+C
Y = A (B+C)
A B C B+C Y
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 1 0
1 0 0 0 0
1 0 1 1 1
1 1 0 1 1
1 1 1 1 1

7. Cont..
3.
Y = 1, jika AB = 1 atau CD = 1
 AB = 1, jika A = 1 dan B = 1
 CD = 1, jika C = 1 dan D = 1
C
D
AB
CD
Y = AB + CD
A
B
A B C D Y
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1

8. ALJABAR BOOLE
Hukum – hukum Aljabar Boole :
1. Komutatif : A + B = B + A
A . B = B . A
2. Asosiatif : A+(B+C) = (A+B)+C
A ( B C ) = ( A B ) C
3. Distributif : A(B+C) = AB + AC
A+(BC) = (A+B).(A+C)

9. Aturan – aturan Aljabar Boole :
1. A . 0 = 0
2. A . 1 = A
3. A . A = A
4. A . A = 0
5. A + 0 = A
6. A + 1 = 1
7. A + A = A
8. A + A = 1
9. A = A
10. A + A B = A + B
11. A + A B = A + B
AND
OR
Ket.
Penjabaran aturan 10 :
A + A B = A (1+B) + A B
= A + AB + A B
= A + B (A + A)
A + A B = A + B 1
Penjabaran aturan 11 :
A + A B = A (1+B) + A B
= A + A B + A B
= A + B (A + A)
A + A B = A + B 1

10. Teorema De Morgan :
1.
2.
A . B = A + B
A + B = A . B
A
B
Y
A
B
Y
A
B
Y= =
A
B
Y
A
B
Y= =
A
B
Y

11. SEKIAN…