Computer Data Representation

• The two's complement notation system is typically used to perform subtraction by using the rules of addition, i.e., preserving addition, where, for example, (5 - 4) is equivalent to (5 + (-4)).

The Basic Strategy of Performing Subtraction by Preserving Addition:

1. Represent both values as positive signed numbers;
2. Decide the minimum bit length required.
3. Convert the subtrahand (quantity to be subtracted) into its negative representation using either of the two methods of 2's complement convertion discussed previously.
4. Then add the two values together.

So, using minimally required number of bits including the sign bit we can perform (5-4) as below:

5₁₀ converts to 0101 (at least a 4-bit pattern including the + sign is required at the outset)

4₁₀ converts to 0100.

so -4₁₀ must be 1100 (after converting the +ive number to its -tive complement)

Add these two together:

• But in this case, we have limited ourselved to a fixed length of 4 bits in this example.
• That being the case, the last carry bit (the 5^th bit) must be "truncated" or discarded as overflow (there is not enough bits allocated).
• The resulting answer is then: 0001 or the signed decimal equivalent of +1