BCD ADDER

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 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

WHY only 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 :-
1) either the carry bit is 1
2) the sum is 1010.
3) or the sum is 1100.

for the numbers which does 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 + Z3 Z2 + Z3 Z1

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