PHYS345 Electricity and Electronics

Quiz 7: Digital Logic

First, find the truth table for this combination of gates:

Two OR gates and an AND gate

Second, show that the following combination is equivalent to the preceding combination of gates:

Two AND gates and an OR gate

Solution

Two OR gates and an AND gate

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

Two OR gates and an AND gate

      A.B A'.C  
A B C F G F+G
0 0 0 0 0 0
0 1 0 0 0 0
1 0 0 0 0 0
1 1 0 1 0 1
0 0 1 0 1 1
0 1 1 0 1 1
1 0 1 0 0 0
1 1 1 1 0 1

Note that the Karnaugh map for the truth table is:

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

The second gate combination may be found directly by boxing the ones with two 1x2 boxes. The first gate combination may be found by boxing the zeros with two 1x2 boxes and then NORing rather than ORing. I derived the alternative combination of gates (in the first part) for the purpose of this quiz by application of DeMorgan's theorems to the second Karnaugh approach.


"http://www.physics.udel.edu/~watson/phys345/quiz/7soln.html"
Last updated November 6, 1998.
Copyright George Watson, Univ. of Delaware, 1998.