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.