Digital Circuit Project
Twisted
Truthtable.pdf
Truth Table
Inputs Outputs
A B C D Y1 Y2 Y3 Y4
0 0 0 0 0 1 1 0 0
1 0 0 0 1 1 0 0 1
2 0 0 1 0 0 0 0 0
3 0 0 1 1 1 0 1 0
4 0 1 0 0 1 0 0 0
5 0 1 0 1 0 0 1 1
6 0 1 1 0 1 1 1 1
7 0 1 1 1 0 0 0 1
8 1 0 0 0 0 1 1 0
9 1 0 0 1 0 1 0 1
10 1 0 1 0 x x x x
11 1 0 1 1 x x x x
12 1 1 0 0 x x x x
13 1 1 0 1 x x x x
14 1 1 1 0 x x x x
15 1 1 1 1 x x x x
K - Maps
SUM of PRODUCTS – for Y1
Map
C'.D' C'.D C.D C.D'
A'.B' 1 1 1 0
A'.B 1 0 0 1
A.B x x x x
A.B' 0 0 x x
Map Layout
C'.D' C'.D C.D C.D'
A'.B' 0 1 3 2
A'.B 4 5 7 6
A.B 12 13 15 14
A.B' 8 9 11 10
Groups
(4,6,12,14) B.D'
(0,1) A'.B'.C'
(1,3) A'.B'.D
Y1 = BD' + A'B'C' + A'B'D
SUM of PRODUCTS – for Y2
Map
C'.D' C'.D C.D C.D'
A'.B' 1 0 0 0
A'.B 0 0 0 1
A.B X X x x
A.B' 1 1 x x
Map Layout
C'.D' C'.D C.D C.D'
A'.B' 0 1 3 2
A'.B 4 5 7 6
A.B 12 13 15 14
A.B' 8 9 11 10
Groups
(8,9,10,11,12,13,14,15) A
(0,8) B'.C'.D'
(6,14) B.C.D'
Y2 = A + B'C'D' + BCD'
SUM of PRODUCTS – for Y3
Map
C'.D' C'.D C.D C.D'
A'.B' 0 0 1 0
A'.B 0 1 0 1
A.B X X x x
A.B' 1 0 x x
Map Layout
C'.D' C'.D C.D C.D'
A'.B' 0 1 3 2
A'.B 4 5 7 6
A.B 12 13 15 14
A.B' 8 9 11 10
Groups
(8,10,12,14) A.D'
(3,11) B'.C.D
(5,13) B.C'.D
(6,14) B.C.D'
Y3 = AD' + B'CD + BC'D + BCD'
SUM of PRODUCTS – for Y4
Map
C'.D' C'.D C.D C.D'
A'.B' 0 1 0 0
A'.B 0 1 1 1
A.B X X x x
A.B' 0 1 x x
Map Layout
C'.D' C'.D C.D C.D'
A'.B' 0 1 3 2
A'.B 4 5 7 6
A.B 12 13 15 14
A.B' 8 9 11 10
Groups
(1,5,9,13) C'.D
(6,7,14,15) B.C
Y4 = C'D + BC
