hw2soln

# hw2soln - (g f’(a,b,c,d = Π M(1,2,4,7,8,11,13,14 2(a We...

This preview shows page 1. Sign up to view the full content.

HW#2 Solutions 1/30/2009 Lecture 4 1. xy + yz + x’z = xy + yz.x + yz.x’ + x’z by 14a = xy + xy.z + x’z + x’z.y = xy + x’z by 13a twice 1. (a) a b c d f Row # 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 2 0 0 1 1 0 3 0 1 0 0 1 4 0 1 0 1 0 5 0 1 1 0 0 6 0 1 1 1 1 7 1 0 0 0 1 8 1 0 0 1 0 9 1 0 1 0 0 10 1 0 1 1 1 11 1 1 0 0 0 12 1 1 0 1 1 13 1 1 1 0 1 14 1 1 1 1 0 15 (b) f = a’b’c’d + a’b’cd’ + a’bc’d’ + a’bcd + ab’c’d’ + ab’cd + abc’d + abcd’ (c) f(a,b,c,d) = Σ m(1,2,4,7,8,11,13,14) (d) f = (a+b+c+d)(a+b+c’+d’)(a+b’+c+d’)(a+b’+c’+d) (a’+b+c+d’)(a’+b+c’+d)(a’+b’+c+d)(a’+b’+c’+d’) (e) f(a,b,c,d) = Π M(0,3,5,6,9,10,12,15) (f) f’(a,b,c,d) = Σ m(0,3,5,6,9,10,12,15)
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (g) f’(a,b,c,d) = Π M(1,2,4,7,8,11,13,14) 2. (a) We can construct the truth table for f. a b c f 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The canonical SOP of f(a,b,c) = Σ m(0,1,2,4,5,6,7) (b) Notice that the original expression is already a SOP and it cannot be further simplified. So simplest SOP of f = a+b’+c’. (c) By considering the ‘0’ output, the canonical POS of f = a+b’+c’....
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.

Ask a homework question - tutors are online