CSE370 Homework 3 Solution

1)    Given f= (a + b' + c')(a' + c')(a+ c + d)(a + b + c + d')

a)  Express f in canonical POS form (use M notation)
f =
Π M(0,1,4,6,7,10,11,14,15)

b)   Express f in canonical SOP form (use m notation)
f = Σm(2,3,5,8,9,12,13)

c)   Express f' in canonical POS form (use M notation)
f' =
Π M(2,3,5,8,9,12,13)

d)   Express f' in canonical SOP form (use m notation)
f = Σm(0,1,4,6,7,10,11,14,15)

2)    Determine a minimized expression for the following using the rules of boolean algebra.

a) F(A,B,C,D) = Σm(1,2,11,13,14,15) + d(0,3,6,10)
Using don't cares (0,3,10),
A'B'C'D' + A'B'C'D + A'B'CD + A'B'CD' + A'BCD' + ABC'D + ABCD + ABCD' +  AB'CD + AB'CD'
A'B' (C'D' + C'D + CD + CD')  + CA(BD' + BD + B'D' + B'D) + D(ABC + ABC')
A'B' +  AC + D(AB(C+C'))
A'B' + AC + ABD

b) G(A,B,C,D) = PM(2,5,6,8,9,10) * D(4,11,12)
Using don't cares(11,12)
First express the function in SOP form.
Σm
(0,1,3,7,13,14,15) + D(4,11,12)
A'B'C'D' + A'B'C'D + A'B'CD + A'BC'D' + A'BCD + ABC'D' + ABC'D + ABCD + ABCD' + AB'CD
A'B'C'(D + D')  + CD(AB + A'B + AB' + A'B') + AB(CD + C'D + CD' + C'D')
A'B'C' + CD + AB

c) Take the complement of the function F from (a) and express it in a minimized SOP form.
F' =
Σm(4,5,7,8,9,12) + d(0,3,6,10)
Using don't cares(0,6)
A'B'C'D' + A'BC'D' + ABC'D' + AB'C'D' + A'BC'D + A'BCD + A'BCD' + AB'C'D
C'D'(A'B' + A'B + AB' + AB) + A'B(CD + C'D + CD' + C'D') + AB'C'(D + D')
C'D' + A'B + AB'C'

3)    a) F(A,B,C,D) =
Σm(3,6,9,12)

b) F(A,B,C,D) = Σm(0,1,2,3,4,6,8,9,12)

4)

 A2 A1 A0 Y1 Y0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0

Y1 = A2
Y2 = A2'A1

5.

6.

7)  a) Z = (  (B Å  C)  *  (A Å B)'  ) +  ( (A Å B) * (B Å C)' )

b)

 A B C Z 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0

c)

Z = Σm(1,3,4,6)
= A'B'C + A'BC + AB'C' + ABC'

d)    =    A'C(B' + B) + AC'(B'+B)
=    A'C + AC'
=    A
Å C

e)