Binary Number System is a base-2 numeral system that uses only two digits: 0 and 1.

It's the foundation of all modern digital systems, including computers, because binary aligns perfectly with the on/off states of electronic switches

Key Characteristics

1. Base: 2

   It uses only two symbols: 0 and 1

2. Positional Value:

   Each digit's position represents a power of 2

Binary to Decimal

1101 → (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

10011 → (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 16 + 0 + 0 + 2 + 1 = 19

Decimal to Binary

Repeated Division Method:

1. Divide the number by 2
2. append the remainder (0 or 1) at the right-end
3. repeat 1,2 until quotient is 0

ex) 15602 into binary