Understanding Binary Math and Base Systems
Binary math operates in Base 2, using only the digits 0 and 1. While decimal is based on powers of 10, binary is built around powers of 2. Each place value in a binary string represents a doubling sequence: 1, 2, 4, 8, 16, 32, and so on.
Positional Values in Base 2
To convert a binary number to decimal, multiply each digit by its positional power of 2, starting with 2⁰ on the far right. For example, the binary value 1011 converts to decimal like this:
(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
= 8 + 0 + 2 + 1 = 11
Binary Arithmetic Rules
Addition Operations
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 1 = 10 (write 0, carry 1)
- 1 + 1 + 1 = 11 (write 1, carry 1)
Subtraction Operations
- 0 - 0 = 0
- 1 - 0 = 1
- 1 - 1 = 0
- 0 - 1 = 1 (after borrowing 1 from left)