Digital Electronics

This topic is an extension of the topic of Boolean Algebra which includes a more thorough description of the category in terms of determining whether a circuit results in a TRUE or FALSE value using truth tables or how to simplify a circuit to as few gates as possible. Electrical engineers use the following symbols to design electrical circuits that are used inside the computer’s hardware. The following table illustrates the equivalent Boolean algebra expression and truth table for each gate.

Definitions

[math]NAME[/math]	[math]GRAPHICAL SYMBOL[/math]	[math]ALGEBRAIC EXPRESSION[/math]	[math]TRUTH TABLE[/math]
BUFFER	Symbol	X = A	truth table
NOT	Symbol	X = ~A	! A X	0 1	1 0
AND	Symbol	X = AB or A*B	A B X	0 0 0	0 1 0	1 0 0	1 1 1
NAND	Symbol	X = ~(AB) or ~(A*B)	A B X	0 0 1	0 1 1	1 0 1	1 1 0
OR	Symbol	X = A+B	A B X	0 0 0	0 1 1	1 0 1	1 1 1
NOR	Symbol	X = ~(A+B)	A B X	0 0 1	0 1 0	1 0 0	1 1 0
XOR	Symbol	X = ~AB+A~B	A B X	0 0 0	0 1 1	1 0 1	1 1 0
XNOR	Symbol	X = AB+~A~B	A B X	0 0 1	0 1 0	1 0 0	1 1 1

Sample Problems

Sample Problem 1

Find all ordered 4-tuples (A, B, C, D), which make the following circuit FALSE:

Solution: This circuit diagram translates to: . The table has the following headings: 1= , 2= , 3= , 4= , and 5= . Thus, the 4-tuples (0,0,0,0), (1,0,0,0), (1,1,0,0), (1,1,0,1), (1,1,1,0), and (1,1,1,1) all make the circuit FALSE.