Page 64 - Digital Electronics by harish

BCD input 7-segment output
A B C D a b c d e f g Display

0 0 0 0 1 1 1 1 1 1 0

0 0 0 1 0 1 1 0 0 0 0

0 0 1 0 1 1 0 1 1 0 1

0 0 1 1 1 1 1 1 0 0 1

0 1 0 0 0 1 1 0 0 1 1

0 1 0 1 1 0 1 1 0 1 1

0 1 1 0 1 0 1 1 1 1 1

0 1 1 1 1 1 1 0 0 0 0

1 0 0 0 1 1 1 1 1 1 1

1 0 0 1 1 1 1 1 0 1 1

Figure : Truth table of BCD to Seven segment decoder

From the truth table, we can find the logic equations for the outputs.

a = + C + C D + B D + B C + B C D + A + A D
b = + D + C + C D + B + B C D + A + A D
c = + D + C D+ B + B D + B C + B C D + A + A
D
d = + C + C D + B D + B C + A + A D
e = + C + B C + A
f = + B + B D + B C + B C D + A + A D
g = C + C D + B + B D + B C + A + A D

By simplifying the above equations using K-map, we get the following simplified logic
equations for the seven segments :
a = A + C + B D +
b = + + C D
c = B + + D
d = + C + B D + A
e = + C
f = A + + B + B

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