Arithmetic Operations & Binary Numbers

Binary numbers are composed of only two digits, 0 and 1, and form the foundation of all modern digital systems. Learning to perform arithmetic operations such as addition, subtraction, multiplication, and division in binary is essential for understanding computer operations. Let’s explore each operation step by step.

1. Binary Addition

Binary addition follows the same principles as decimal addition but with a base of 2. The rules for binary addition are:

Binary Addition Rule	Result	Carry
0 + 0	0	0
0 + 1	1	0
1 + 0	1	0
1 + 1	0	1

Example: Add 1011 and 1101.

  1011

+1101

---------

 11000

The result is 11000.

2. Binary Subtraction

Binary subtraction uses the borrowing method, similar to decimal subtraction. The rules are:

Binary Subtraction Rule	Result	Borrow
0 - 0	0	0
1 - 0	1	0
1 - 1	0	0
0 - 1	1	1

Example: Subtract 1010 from 1101.

  1101

- 1010

----------

   0011

The result is 0011.

3. Binary Multiplication

Binary multiplication is simpler than decimal multiplication, as it only involves multiplying by 0 or 1. The rules are:

Binary Multiplication Rule	Result
0 × 0	0
0 × 1	0
1 × 0	0
1 × 1	1

Example: Multiply 101 by 11.

     101

×     11

----------

      101

+  1010

----------

     1111

The result is 1111.

4. Binary Division

Binary division is similar to decimal division and involves repeated subtraction. The process includes:

1. Dividing the dividend by the divisor.

2. Writing down the quotient.

3. Subtracting the product of the divisor and the quotient from the dividend.

4. Repeating until the remainder is smaller than the divisor.

Example: Divide 1101 by 10.

  1101 ÷ 10

   ------------

   10 | 1101

        -10

   -----------

           10

          -10

   -----------

             1 (remainder)

The quotient is 110, and the remainder is 1.

Key Points to Remember:

1. Binary arithmetic relies on base-2 rules.

2. Always align binary numbers properly before performing operations.

3. Double-check carries and borrows during addition and subtraction.

4. Binary multiplication and division are systematic and straightforward with practice.

Understanding these operations lays the groundwork for further studies in computer architecture, digital circuits, and programming.