## PHYS345 Electricity and Electronics

Quiz 8: Digital Logic

Simplify the following expression using Karnaugh mapping:

A.B + A'.C + B.C

The truth table may be constructed as follows. Note that I have changed to a format for the inputs that is better suited for creating the truth table for Karnaugh mapping. However the usual incremental sequence from 000 to 111 is also perfectly acceptable.

A     B     C   D=
A.B
E=
A'.C
F=
B.C
D+E+F
0 0 0 0 0 0 0
0 1 0 0 0 0 0
1 1 0 1 0 0 1
1 0 0 0 0 0 0
0 0 1 0 1 0 1
0 1 1 0 1 1 1
1 1 1 1 0 1 1
1 0 1 0 0 0 0

C 0  1
AB\
00     0   1
01     0   1
11     1   1
10     0   0

Note that since the expression is a sum-of-products you could have created the truth table for Karnaugh mapping directly!

Boxing the ones with the fewest number of supercells:

C 0  1
AB\
00     0   1
01     0   1
11     1   1
10     0   0

The red cells correspond to A' .C.
The green cells correspond to .B.
Thus the truth table can be created with (A' .C) + (A .B);
the third term in the original expression is apparently redundant.
Reexamination of the truth tables bears this out.

"http://www.physics.udel.edu/~watson/phys345/quiz/09soln.html"
Last updated November 11, 1999.
Copyright George Watson, Univ. of Delaware, 1999.