Binary Number System

Overview

Binary is the fundamental number system used in digital electronics, using only two digits (0 and 1) to represent all numbers. This system directly corresponds to the two voltage levels in digital circuits, making it the natural choice for digital systems. Each position in a binary number represents a power of 2, and the simplicity of binary arithmetic makes it ideal for computer calculations.

Detailed Explanation

Binary Position Values

Position:  2⁷  2⁶  2⁵  2⁴  2³  2²  2¹  2⁰
          128  64  32  16   8   4   2   1
Value:     1   0   1   1   0   1   0   1
         (181 decimal)

Binary Math

Addition:    Multiplication:
  1011         1011
+ 0110       × 0110
------       ------
  10001        0000
               1011
              1011
             0000
            -------
             100001

Quick Tips

1. Common Powers of 2:

2⁰  = 1
2¹  = 2
2²  = 4
2³  = 8
2⁴  = 16
2⁵  = 32
2⁶  = 64
2⁷  = 128
2⁸  = 256
2⁹  = 512
2¹⁰ = 1024

Practice Problems

1. Convert to decimal:
   • 1010 1011
   • 1111 0000
   • 0111 1111

← Back to Minor - Digital Electronics