- 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
Before we talk about BCD addition and subtraction using Excess 3 code, let’s understand what Excess 3 code is. It’s a binary code created by adding 3 to the decimal equivalent of a binary number, then converting it back to binary. For any binary number, first convert it to a decimal number, add 3, and then convert it back to binary to get the excess 3 equivalent. Now, let’s see how to perform BCD addition and subtraction using this method.
Excess 3 Code Addition
Adding numbers in excess 3 code is straightforward. We’ll explain it step-by-step.
Step 1
Convert the numbers to be added into their excess 3 forms by adding 0011 to each four-bit group.
Step 2
Now the two numbers are added using the basic laws of binary addition, there is no exception for this method.
Step 3
Add 0011 to the groups that generated a carry, and subtract 0011 from the groups that did not.
Step 4
The result which we have obtained after this operation is in Excess 3 form and this is our desired result
Example
To understand the Excess 3 Code Addition method better we can observe the method with the help of an example,
Let us take two numbers which we will to add.
0011 0101 0110 and 0101 0111 1001 are the two binary numbers. Now following the first step we take the excess 3 form of these two numbers which are 0110 1000 1001 and 1000 1010 1100, now these numbers are added following the basic rules of addition.
Now adding 0011 to the groups which produces a carry and subtracting zero from the groups which did not produced carry we get the result as 1100 0110 1000 is the result of the addition in excess 3 code and the BCD answer is 1001 0011 0101.
Excess 3 Code Subtraction
Similarly binary subtraction can be performed by Excess 3 Code Subtraction method. The operation is illustrated with the help of some steps.
Step 1
Like the previous method both the numbers have to be converted into excess 3 code
Step 2
Following the basic methods of binary subtraction, subtraction is done.
Step 3
Subtract ‘0011’ from each BCD four-bit group in the answer if the subtraction operation of the relevant four-bit groups required a borrow from the next higher adjacent four-bit group.
Step 4
Add ‘0011’ to the remaining four-bit groups, if any, in the result.
Step 5
Finally we get the desired result in excess 3 code.
Example
Again an example will make the understanding very easy for us.
Let us take the numbers
0001 1000 0101 and 0000 0000 1000 now the excess 3 equivalent of those numbers are 0100 1011 1000 and 0011 0011 1011
Now performing the operation of binary subtraction we get
Now in the above mentioned operation the least significant column which needed a borrow and the other two columns did not need borrow. Now we have to subtract 0011 from the result of this column and add 0011 to the other two columns, we get 0100 1010 1010. This is the result expressed in excess 3 codes. And the binary result is 0001 0111 0111
