BCD to 9′s complement converter

(i) No. of inputs and outputs

Number of inputs = 4

Number of outputs = 4

(ii)Assigning letter symbols

Symbols of inputs – A, B, C, D

Symbols of outputs – W, X, Y, Z

(iii)Truth table

INPUT

OUTPUT

A

B

C

D

W

X

Y

Z

0

0

0

0

1

0

0

1

0

0

0

1

1

0

0

0

0

0

1

0

0

1

1

1

0

0

1

1

0

1

1

0

0

1

0

0

0

1

0

1

0

1

0

1

0

1

0

0

0

1

1

0

0

0

1

1

0

1

1

1

0

0

1

0

1

0

0

0

0

0

0

1

1

0

0

1

0

0

0

0

 

(iv)Boolean equation

Z

All the entries of Z are compliment of the entries of D.So,

Z=D’

Y

All the entries of Y and C are same in the truth table.So,

Y=C

X

BCD to 9s complement k map

X = BC’+ B’C = B(XOR)C

W

From the truth table,

W = A’B'C’D’ + A’B'C’D = A’B'C’(D’+D) = A’B'C’

(v)Logic Diagram

BCD to 9's complement circuit

10 thoughts on “BCD to 9′s complement converter

    • Hi Kirti,
      If you observe the truth table, there are only two instances where W is true. So, solving it using boolean algebra is much simpler. However, solving it using a K-Map would obtain the same result.