The binary number system

The decimal system uses ten digits and weights 10⁰, 10¹, 10², ... For example 17 = 1 × 10¹ + 7 × 10⁰. The binary system has two digits (0 and 1) and weights 2⁰, 2¹, 2², 2³ ... For example:

• 3 = 1 × 2¹ + 1 × 2⁰ = 11₂
• 5 = 1 × 2² + 0 × 2¹ + 1 × 2⁰ = 101₂
• 13 = 8 + 4 + 0 + 1 = 1101₂
• 10110₂ = 16 + 0 + 4 + 2 + 0 = 22.
• With n binary digits (bits) we can represent 2ⁿ different values: 8 bits give 256 values.

• An analog-to-digital converter (ADC) encodes the natural signal into binary code; at the receiver a digital-to-analog converter (DAC) decodes it back.
• Pictures are divided into tiny elements called pixels and each is coded.