Question

Design a 9’s complement of a Binary Coded Decimal

Answer 1

Step 1 : Truth Table for BCD to 9's complement output

BCD NUMBER	A B C D	9's COMPLEMENT OF NUMBER	W X Y Z
0	0 0 0 0	9	1 0 0 1
1	0 0 0 1	8	1 0 0 0
2	0 0 1 0	7	0 1 1 1
3	0 0 1 1	6	0 1 1 0
4	0 1 0 0	5	0 1 0 1
5	0 1 0 1	4	0 1 0 0
6	0 1 1 0	3	0 0 1 1
7	0 1 1 1	2	0 0 1 0
8	1 0 0 0	1	0 0 0 1
9	1 0 0 1	0	0 0 0 0

Step 2 : Boolean Expression from the Truth Table

The bit combination assigned to binary code to 9’s complement. Since each code uses four bits to represent a decimal digit. There are four inputs and outputs. The inputs variable is designated as A, B, C, D and the output variables are W, X, Y, Z from the truth table, combinational circuit is designed. The Boolean functions are obtained from K-Map for each output variable.

Binary to 9’s Complement conversion: -

To obtain the 9’s complement of any number we have to subtract the number with (-1) where n=number of digits in a number.

Examples: - Consider the decimal number 8.) = (Binary code: - 1000)

9’s complement: - 0001

Boolean equation from truth table: -

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

X=BC’+B’C

Y=C

Z=D’

Step 3 : Circuit Diagram for BCD To 9's Complement