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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 .


Decimal BCD
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001


up to 9 the bcd representation is same as the decimal representation and after the 9 <

Decimal BCD
10 0001 0000
11 0001 0001
12 0001 0010
13 0001 0011
14 0001 0100
15 0001 0101
16 0001 0110
17 0001 1000
18 0001 1000
19 0001 1001

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



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