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