written 6.0 years ago by |
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 .
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 the 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 0111 |
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
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