- Excess 3 Code Definition: Excess 3 code is defined as a binary code made by adding 3 to the decimal equivalent of a binary number and then converting it back to binary.
- Excess 3 Addition Process: Convert numbers to excess 3 by adding 0013 to each four-bit group, perform binary addition, and adjust based on carry generation.
- Carry Adjustment in Addition: Add 0011 to groups that generate a carry and subtract 0011 from groups that don’t to get the final excess 3 result.
- Excess 3 Subtraction Process: Convert numbers to excess 3, perform binary subtraction, and adjust based on borrow requirements.
- Borrow Adjustment in Subtraction: Subtract 0011 from groups that needed a borrow and add 0011 to groups that didn’t to get the final excess 3 result.
Excess 3 Code
This page is about BCD addition and subtraction with Excess 3 code. Excess 3 code stores each decimal digit as the 4-bit binary of that digit plus 3 (0 is 0011, 9 is 1100). For any binary number already grouped as BCD digits, add 0011 to each group to form Excess-3, then add or subtract as below.
Excess 3 Code Addition
To add two Excess-3 numbers, add them as ordinary binary, then correct each 4-bit group by +0011 if it produced a carry and by -0011 if it did not.
Step 1
If the addends are BCD, form Excess-3 by adding 0011 to each four-bit group.
Step 2
Add the two Excess-3 numbers with the ordinary rules of binary addition.
Step 3
Add 0011 to each group that generated a carry. Subtract 0011 from each group that did not.
Step 4
The corrected word is the Excess-3 sum. Subtract 0011 from each group if a BCD reading is needed.
Example
Excess 3 Code Addition of 0011 0101 0110 and 0101 0111 1001 (BCD 356 and 579).
Those two binary numbers in Excess-3 are 0110 1000 1001 and 1000 1010 1100. Add them with the same binary rules.
Add 0011 to each group that produced a carry and subtract 0011 from each group that did not. The Excess-3 sum is 1100 0110 1000. The BCD sum is 1001 0011 0101 (935).
Excess 3 Code Subtraction
binary subtraction of Excess-3 numbers uses the Excess 3 Code Subtraction method below.
Step 1
Convert both numbers to Excess-3 by adding 0011 to each BCD group.
Step 2
Subtract with the ordinary binary rules.
Step 3
Subtract ‘0011’ from each BCD four-bit group that borrowed from the next higher four-bit group.
Step 4
Add ‘0011’ to the remaining four-bit groups, if any, in the result.
Step 5
The corrected word is the difference in excess 3 code.
Example
Subtract 0001 1000 0101 minus 0000 0000 1000 (BCD 185 minus 8).
0001 1000 0101 and 0000 0000 1000 in Excess-3 are 0100 1011 1000 and 0011 0011 1011
Ordinary binary subtraction gives
The right-hand group borrowed; the other two did not. Subtract 0011 from that group and add 0011 to the other two. The Excess-3 difference is 0100 1010 1010, written in excess 3 codes. The BCD difference is 0001 0111 0111.
