BCD ADDER:

A BCD adder is a combinational circuit which adds two BCD numbers.

WHAT ARE BCD NUMBERS ?

BCD is a class of encoding in which each decimal digit is represented by some fixed number of bits. Usually, 4 or 8 bits are used .

up to 9, the BCD representation is the same as the decimal representation and after the 9

the first 4 digits in BCD representation is used to show the first digit in decimal and next four digits in BCD are used to represent next digit in decimal.

TRUTH TABLE

4 BIT ADDER CAN NOT BE USED?

when we provide two 4 bits BCD number to the 4-bit adders, the output exceeds the BCD range or called BCD representation. WE WANT TO OUTPUT ALSO IN BCD. but when we directly take the output of the 4 bit adder then it will be a invalid representation.

Therefore we need some mechanism through which we can change the output of the 4 bit adder into a valid BCD representation .

if you carry fully see , that the up to when the sum is 9 , the BCD representation is same as the binary representation .

when the sum exceed the 9 , the following condition occur :-

• either the carry bit is 1
• the sum is 1010
• or the sum is 1100

for the numbers which do not satisfy the condition of BCD, 6 is added. see in the table, when the sum is 01010 the bcd representation is obtained by adding 6 ., so the representation in BCD is 1 0000.

the condition when 6 is to be added is

$F = CO + Z_3 Z_2 + Z_3 Z_1$

this can be easily obtained by K - map. where CO is the output carry . and the z3 is the 4 bit, z2 the bit 3 and similarly z1 bit 2