hw1soln

# hw1soln - by 10b twice = b a’.c by 12b = a’.c b = RHS...

This preview shows pages 1–2. Sign up to view the full content.

HW#1 Solutions 1/23/2009 1. (a) (b) (c) f = x 2. (a) F = (A.B)’.(A.B + B.C) (b) A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 3. (a) F = x’.y (b) Lecture 4 1. (a) A b c (a+b).a’ + c.b (a’+c).b 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 (b) LHS = (a+b).a’ + c.b = a’.(a+b) + c.b by 10a = a’.((a’)’+b) + c.b by 9 = a’.b + c.b by 16b = b.a’ + b.c by 10a twice = b.(a’ + c) by 12a = (a’ + c).b = RHS by 10a x y f 0 0 0 0 1 0 1 0 1 1 1 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(c) The dual theorem is: (a.b +a’).(c+b) = a’.c + b LHS = (a.b +a’).(c+b) = (a’ + a.b).(c+b) by 10b = (a’ + (a’)’.b).(c+b) by 9 = (a’ + b).(c+b) by 16a = (b + a’).(b+c)
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: by 10b twice = b + a’.c by 12b = a’.c + b = RHS by 10b 2. (a) (b) Cost = # gates + # inputs = 9 + 23 = 32 (c) (Note that some obvious steps are skipped in the following.) f = (a’bc’ + a’bc) + (a’b’c + a’bc) + (ab’c + abc) duplicating a’bc by 7b = a’b + a’c + ac by 14a three times = a’b + c by 14a again (d) (e) Cost = 3 + 5 = 8...
View Full Document

## This note was uploaded on 04/07/2009 for the course CPR E 281 taught by Professor Chu,chris during the Spring '07 term at Iowa State.

### Page1 / 2

hw1soln - by 10b twice = b a’.c by 12b = a’.c b = RHS...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online