Question

1. Consider the following Boolean expression (a + b) ^. (a + c). Provide a simpler expression (fewer gates) that is equivalent. Show that your expression is equivalent by building truth tables for both expressions in the same way as we've done before. 1a. Imagine that you have designed a circuit that uses N expressions of the form (a + b) ^. (a + c). We replace each of these with your solution to question 1. How many fewer transistors will we use when building this circuit? Briefly explain.

Answer 1

simpler expression for (a+b).(a+c) will be a+bc

truth table for (a+b)(a+c)

a	b	c	a+b	a+c	(a+b)(a+c)
0	0	0	0	0	0
0	0	1	0	1	0
0	1	0	1	0	0
0	1	1	1	1	1
1	0	0	1	1	1
1	0	1	1	1	1
1	1	0	1	1	1
1	1	1	1	1	1

truth table for a+bc

a	b	c	bc	a+bc
0	0	0	0	0
0	0	1	0	0
0	1	0	0	0
0	1	1	1	1
1	0	0	0	1
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

for (a+b)(a+c) we will need 5 transistors whereas for a+bc we will need 4 transistors so for N expressions we willl need n fewer transistors