Digital Logic

Digital Logic

The Basic Logic Gates

Boolean algebra uses variables and operators in representing the logic circuits. However, the variables have only one value which is 0 and 1. The complement of a variable is shown by a bar over the letter such as Ā or apostrophe (A’). The table below will summarizes logic gates as the symbol of the functions in Boolean expressions in an easier way for understanding.

Positive and Negative logic

It is said that in positive logic, TRUE is represented by “1” and FALSE represented by “0”. Table below will display the truth table for the NAND function.

A)

Truth Table
Input A	Input B		NAND
F	F		T
F	T		T
T	F		T
T	T		F

B)

Truth Table
Input A	Input B		NAND
0	0		1
0	1		1
1	0		1
1	1		0

As you can see, (b) is obtained directly from (a) by substitute F=0 and T=1. This is known as the positive logic. Logic schemes can also be implemented using negative logic which is the other way round whereas F=1 and T=0. By making such substitution, table (c) will be obtained.

C)

Truth Table
Input A	Input B		Output Z
T	T		F
T	F		F
F	T		F
F	F		T

The above table showed that output Z is the NOR function, and so leads to the conclusion which is a positive logic NAND gate can also regarded as a negative logic NOR gate. Vice versa, a positive logic NOR gate can also be regarded as a negative logic NAND gate.

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