To convert binary to decimal, multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right). Then, add up all these values.
What Is Binary and Decimal?
- Binary: It’s a system of numbers that only uses two digits: 0 and 1. Think of it as a language for computers!
- Decimal: The number system we use every day, which has ten digits (0 to 9).
How Does Binary to Decimal Conversion Work?
The main idea is to convert a binary number (made up of 0s and 1s) into a decimal number. Binary uses powers of 2 to represent values, starting from the rightmost digit (also called the least significant bit).
Simple Step-by-Step Conversion
Let’s use a binary number example: 1011.
Write down the binary number: 1011
List the power of 2s below each digit: Starting from the right, list the powers of 2 as follows: Digit 1 1 0 1 Power 2³ 2² 2¹ 2⁰ Value 8 4 0 1
Multiply each binary digit by its corresponding power of 2:
- Leftmost ‘1’: 1 × 2³ = 8
- Next ‘0’: 0 × 2² = 0
- Next ‘1’: 1 × 2¹ = 2
- Rightmost ‘1’: 1 × 2⁰ = 1
Add up all the values:
8 + 0 + 2 + 1 = 11
So, the binary number 1011 converts to the decimal number 11.
Quick Examples
Binary: 1101
- Positions: 2³, 2², 2¹, 2⁰
- Values: 1×8, 1×4, 0×2, 1×1
- Calculation: 8 + 4 + 0 + 1 = 13
Binary: 1001
- Positions: 2³, 2², 2¹, 2⁰
- Values: 1×8, 0×4, 0×2, 1×1
- Calculation: 8 + 0 + 0 + 1 = 9
Quick Tips
- Start from the rightmost digit: This is always multiplied by 2⁰ (which equals 1).
- Move left: Multiply each digit by increasing powers of 2 (1, 2, 4, 8, etc.).
- Add the results: The sum gives you the decimal value.
Now you have the basics to convert any binary number into decimal! Keep practicing with different binary numbers to get the hang of it.