ECPE 2504
Introduction to Computer Engineering

Examples: Combinational Logic and Boolean Algebra
Part 2. Definition of the Logic Function

For this example, we consider the following Boolean logic function, F:

Starting equation for F

F is a function of the four Boolean variables a, b, c, and d and it includes the three basic logic operations, AND, OR, and INVERT. Function F can also be defined by a truth table. The truth table below is derived from the expression for F above.

a
b
c
d
bd
bd'
(bd+bd')
a'(bd+bd')
(a+b+d)'
(c'+d)
[b+(c'+d)]'
ab'c'd
F
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
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Comments to: midkiff@vt.edu
Last updated: January 25, 2000
http://fiddle.visc.vt.edu/courses/ecpe2504/combinational/logic_02.html
© 1996, 2000, Scott F. Midkiff