Binary Number System - JSS3 Mathematics Lesson Note

The binary number system is a base-2 numeral system that uses only two digits, 0 and 1. It is the foundation of all modern computing systems and digital electronics.

Key Concepts:

Digits (Bits): Each digit in a binary number is called a bit. A bit can either be 0 or 1.

Place Values: Each bit in a binary number has a place value that is a power of 2.

Examples:

Binary to Decimal Conversion:

Binary: 1011

Decimal: 

1×2^3+0×2^2+1×2^1+1×2^0

Calculation: 

1×8+0×4+1×2+1×1=8+0+2+1=11
 

Decimal to Binary Conversion:

Decimal: 13

Find the highest power of 2 less than 13: 

2^3=8

13 - 8 = 5 → next highest power of 2: 

2 ^2 =4

5 - 4 = 1 → next highest power of 2: 

2^0 =1

Combine the powers: 

2^3+2^2+2^0  → Binary: 1101