Binary to Decimal Converter

About Binary to Decimal Conversion

Binary to decimal conversion is the process of converting a number from the binary (base-2) numeral system to the decimal (base-10) numeral system. This is a fundamental operation in computer science and digital electronics, as computers use binary to represent all data and perform calculations.

How to Convert Binary to Decimal

To convert a binary number to decimal, follow these steps:

1. Write down the binary number.
2. Starting from the right (least significant bit), assign each digit a position number starting at 0.
3. Multiply each binary digit by 2 raised to the power of its position number.
4. Sum all the results to get the decimal equivalent.

Example Conversion:

Convert binary 1010 to decimal:

1 × 2³ = 8
0 × 2² = 0
1 × 2¹ = 2
0 × 2⁰ = 0
            

Sum: 8 + 0 + 2 + 0 = 10 (decimal)

Signed Binary Numbers (Two's Complement)

For signed binary numbers using two's complement representation:

• The leftmost bit (most significant bit) represents the sign (0 for positive, 1 for negative).
• To convert a negative binary number, invert all the bits and add 1 to get the positive equivalent, then add a negative sign.
• Example: 11111111 in 8-bit two's complement is -1 in decimal.

Binary Number System Basics

The binary number system is a base-2 numeral system that uses only two digits: 0 and 1. Each digit in a binary number is called a bit. Binary is the fundamental language of computers and digital systems.

Key Properties:

• Base: 2
• Digits: 0, 1
• Each position represents a power of 2
• Widely used in computing and digital electronics

Common Uses

Binary to decimal conversion is essential for:

• Understanding how computers represent and process numbers
• Debugging low-level software and hardware
• Working with binary data in programming
• Digital circuit design and analysis
• Computer science education