DIGITAL LOGIC

Login design.

·           Digital electronics operate with only two voltage levels

-          high voltage and a low voltage

·           Computer used binary system (1,0)

·           Combinational logic block contains no memory

·           Logic block with n inputs, there are 2^nd entries (possibility) in the truth table.

Boolean algebra.

• P1: X = 0 or X = 1
• P2: 0 . 0 = 0 
• P3: 1 + 1 = 1 
• P4: 0 + 0 = 0 
• P5: 1 . 1 = 1 
• P6: 1 . 0 = 0 . 1 = 0 
• P7: 1 + 0 = 0 + 1 = 1

Laws of Boolean algebra.

Example.

Basic Logic Gates.

Boolean Equation Forms.

Sum-of-product (SOP)

-          Combination of input values that produce 1s is convert into equivalent variables, ANDed together then ORed with other combination variables with same output.

-          SOP is easier to derive from truth table.

Example:

F = ABC + (ABC)’

The truth table:

A	B	C	ABC	(ABC)’	F
0	0	0	0	1	1
0	0	1	0	1	1
0	1	0	0	1	1
0	1	1	0	1	1
1	0	0	0	1	1
1	0	1	0	1	1
1	1	0	0	1	1
1	1	1	1	0	1

SOP expression:

F = ABC + (ABC)’

Product-of-sums (POS)

-          Input combinations that produce 0 in sums terms (ORed variables) are ANDed together.

-          Convert input values that produce 0s into equivalent variables, ORed the variables, then ANDed with other ORed.

-          Usually are if more 1s produce in output function.

Example:

F = (A + B + C)(A + B + C’)(A + B’ + C)(A’ + B + C)

A	B	C	F
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	1
1	0	1	0
1	1	0	1
1	1	1	1

POS expression:

F = (A + B + C)(A + B + C’)(A + B’ + C)(A’ + B + C)

Post by Marissa Aefdiani Effendi (B031210235)