Homework 2 Examples
Purposes:
(1) work with combinational logic;
(2) work with sequential logic.
1. Consider A*( (~A) + B ) = A*B. Show by truth table that this is true.
A B | ~A | ~A + B | A*(~A+B) | A*B
-----+----+--------+----------+-----
0 0 | 1 | 1 | 0 | 0
0 1 | 1 | 1 | 0 | 0
1 0 | 0 | 0 | 0 | 0
1 1 | 0 | 1 | 1 | 1 true because the table is an
^ ^ exhaustive enumeration and the
\______/ last two columns are the same
Show by algebraic manipulation that this is true.
A*( (~A) + B )
= A*(~A) + A*B by distributive postulate
= 0 + A*B by inverse postulate
= A*B by identity postulate
2. Determine the simplest logic expression for the values in this Kmap:
\BC
A\ 00 01 11 10
+----+----+----+----+ _ _ _ _ _ _ _ _
0 | 1 | 1 | 0 | 0 | sum of products = A*B*C + A*B*C + A*B*C + A*B*C
+----+----+----+----+ _
1 | 1 | d | d | 1 | don't cares = A*B*C + A*B*C
+----+----+----+----+
_
simplified expression = A + B (treat both don't cares as true)
3. [see pdf file for examples of sequential logic questions]