In this article we are going to discuss about bcd to excess 3 code conversion. Before we start, make sure you have a clear concept of number system and decimal to binary conversion.
Unlike other conversions BCD to excess 3 code conversion is super easy. BCD can be converted to excess 3 code by adding number 3 to its decimal value. Suppose we need to convert 1 ( 0001 ) to its excess 3 code. Adding decimals, 1 + 3 = 4. So access 3 code for 1 is 4 ( 0100 ).
BCD to excess 3 code conversion
The code conversions from 1 to 15 is shown in the table below.
D | BCD | Excess 3 code | E | ||||||
| A | B | C | D | W | X | Y | Z |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 3 |
1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 4 |
2 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 5 |
3 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 6 |
4 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 7 |
5 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 8 |
6 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 9 |
7 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 10 |
8 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 11 |
9 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 12 |
10 | Don’t Care Condition | ||||||||
11 | |||||||||
12 | |||||||||
13 | |||||||||
14 | |||||||||
15 | |||||||||
Here D is decimal number, A, B, C & D are BCD, W, X, Y & Z are excess 3 code of BCD & E is equal to Decimal + 3. The binary coded decimal of E is excess 3 code.
Output equations
The output will be written only where logic 1 is obtained in excess 3 code. Don’t care ( d ) will be considered with all. The output can be written as –
W = Σ m ( 5, 6, 7, 8, 9 ) + d ( 10, 11, 12, 13, 14, 15 )
X = Σ m ( 1, 2, 3, 4, 9 ) + d ( 10, 11, 12, 13, 14, 15 )
Y = Σ m ( 0, 3, 4, 7, 8 ) + d ( 10, 11, 12, 13, 14, 15 )
Z = Σ m ( 0, 2, 4, 6, 8 ) + d ( 10, 11, 12, 13, 14, 15 )
K Map for W
Output equation
Y ( W ) = A + B ( C + D )
K Map for X
Output equation
Y ( X ) = A’B’ ( C + D ) + BC’D’ + AD
K Map for Y
Output equation
Y ( Y ) = C’D’ + CD
K Map for Z
Output equation
Y ( Z ) = C’D’ + CD’ = D’ ( C’ + C ) = D’
Example
Q. Convert BCD ( 0100 ) to excess 3 code.
– we know, decimal of BCD ( 0100 ) is 4. So 4 + 3 = 7 ( 0111 ).
So excess 3 code of BCD ( 0100 ) is ( 0111 ).
Excess 3 code to BCD
The process of converting excess 3 code back to BCD is just opposite. Here we subtract 3 from the excess 3 code to get the Binary Coded Decimal.
The table below shows excess 3 code and their BCD.
D | Excess 3 Code | BCD | E | ||||||
| W | X | Y | Z | A | B | C | D |
|
0 | 0 | 0 | 0 | 0 | X | X | X | X | |
1 | 0 | 0 | 0 | 1 | X | X | X | X |
|
2 | 0 | 0 | 1 | 0 | X | X | X | X |
|
3 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
4 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
5 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 2 |
6 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 3 |
7 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 4 |
8 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 5 |
9 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 6 |
10 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 7 |
11 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 8 |
12 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 9 |
13 | 1 | 1 | 0 | 1 | X | X | X | X |
|
14 | 1 | 1 | 1 | 0 | X | X | X | X |
|
15 | 1 | 1 | 1 | 1 | X | X | X | X |
|
Here D is the decimal number, W, X, Y & Z are the excess 3 code of the decimal numbers. A, B, C & D are Binary Coded Decimals. E is equal to decimal ( D ) – 3, that starts from 3 – 3 = 0.
Example
Convert excess 3 code ( 0110 ) to BCD.
– We know, according to table given above.
Decimal number of excess 3 code ( 0110 ) is 6.
So 6 – 3 = 3 ( 0011 ).
So BCD of excess 3 code ( 0110 ) is ( 0011 )
Author
Akash Sharma
Half adder and full adder is a part of combinational circuits. Combinational circuits are those whose output characteristics depends on their input levels at a particular time.
Excellent explanation 👍
Thank You