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Design a BCD to excess 3 code converter using minimum number of NAND gates.
Hint: use k map techniques.
Ans. Firstly we make the truth table:
BCD no
A B C D
EXCESS-3 NO
W X Y Z
0 0 0 0
0 0 1 1
0 0 0 1
0 1 0 0
0 0 1 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
After that by using K maps we can get simplified functions for w, x, y, z shown below as:
NAND gate implementation for simplified function
W = BD + AD + AB' + BCThrough complementing twice we findW = ((BD + AD + AB' + BC)')'
= ((BD)' . (AD)' . (AB')' . (BC)')' X = BC'D + B'D + B'C
Through complementing twice we findX = BC'D + B'D + B'C
= ((BC'D)' . (B'D)' . (B'C)')'
Y = C'D' + CD
= ((C'D')' + (CD)')'
Z = D'
Logic diagram for BCD to excess 3 code converter using minimum number of NAND gates
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