Polytechnic
Institute
of
NYU
Page
1
of
2
Handout
No
:
7
October
1,
2009
Function f(A, B, C, D) in Different Representations
CS2204
DIGITAL LOGIC & STATE MACHINE DESIGN
FALL 2009
f(A, B, C, D)
M(0,2,4,6,8,10,11,12,14)
∏
=
The maxterm list :
f(A,B,C,D)
A
A
B
B
C
C
D
D
Digital Circuit
Black Box :
Double-rail Inputs
f(A,B,C,D)
A
B
C
D
Digital Circuit
Double-rail Inputs
Black Box :
A B C D
f(A, B, C, D)
0 0 0 0
0
0 0 0 1
1
0 0 1 0
0
0 0 1 1
1
0 1 0 0
0
0 1 0 1
1
0 1 1 0
0
0 1 1 1
1
1 0 0 0
0
1 0 0 1
1
1 0 1 0
0
1 0 1 1
0
1 1 0 0
0
1 1 0 1
1
1 1 1 0
0
1 1 1 1
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Truth Table :
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
The canonical SOP expression :
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)(
A+
B+C+D)(
A+
B+
C+D)
The canonical POS expression :
f(A, B, C, D)
m(1,3,5,7,9,13,15)
∑
=
The minterm list :
f(A, B, C, D)
= D(AB +
C) +
ABCD +
A
B D
A nonminimal expression for function f
= ABD +
CD +
AD(
B + BC)
k(m + s) = km + ks
= ABD +
CD +
AD(
B + C)
k +
km = k + m
= ABD +
CD +
A
B D +
ACD
k(m + s) = km + ks
= ABD +
A
B D + D(
C + C
A)
k(m + s) = km + ks
= ABD +
A
B D +
CD +
AD
k +
km = k + m
&
k(m + s) = km + ks
= ABD +
CD +
AD(1 +
B)