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BINARY SUBTRACTION

The basic rules for binary subtraction are listed in the table below:

Case Input Sum Carry

1 0 – 0 0 0

2 1 – 0 1 0

3 1 – 1 0 0

4 0 – 1 1 *1

* To subtract a higher digit from a lower digit, i.e., 1 from 0, one has to borrow from the left column.

Example 1 Example 2 Example 3

Compute (1110) + (101) Compute (10101) + (1010) Compute (11101) + (10011)
2 2 2 2 2 2
0 10 0 10 0 10 0 10
1 1 1 0 1 0 1 0 1 1 1 1 0 1
– 1 0 1 – 1 0 1 1 – 1 0 0 1 1
1 0 0 1 1 0 1 1 0 1 0 1 0

BINARY MULTIPLICATION
The Binary multiplication is similar to the decimal multiplication. It is simpler than decimal multiplication
because only 0 and 1 are involved. The basic rules for binary multiplication are listed in the table below:

Case Input Multiplication

1 0 × 0 0

2 1 × 0 0

3 0 × 1 0

4 1 × 1 1

Example 1 Example 2 Example 3
Compute (110) × (11) Compute (1101) × (10) Compute (1001) × (101)
2 2 2 2 2 2
1 0 0 1
1 1 0 1 1 0 1 × 1 0 1
× 1 1 × 1 0 1 0 0 1

1 1 0 0 0 0 0 0 0 0 0 ×
1 1 0 × 1 1 0 1 × 1 0 0 1 × ×
1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1

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