Binary to Decimal Converter

How to Convert Binary to Decimal?

Binary to decimal conversion transforms base-2 numbers (using only 0 and 1) into base-10 numbers (0-9). Each binary digit represents a power of 2, starting from the rightmost digit as 2⁰.

Conversion steps:
1. Write down the binary number
2. Multiply each digit by 2 raised to its position power (from right to left, starting at 0)
3. Add all the results together

Example: Convert 1011 to decimal:
1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11

What is a binary number?

Binary is a base-2 numeral system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital electronics. Each binary digit (bit) represents a power of 2. Binary numbers are used in computing because digital circuits have two states: on (1) and off (0).

How do I convert binary to decimal manually?

To convert binary to decimal manually:
1. Write the binary number
2. Number each digit from right to left, starting with 0
3. For each digit that is 1, calculate 2 raised to that position number
4. Add all these values together

Example for binary 1101:
Position: 3 2 1 0
Binary: 1 1 0 1
= 1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 8 + 4 + 0 + 1
= 13 (decimal)

What is the largest binary number?

There's no largest binary number - they can be infinitely long, just like decimal numbers. However, in computer systems, binary numbers are limited by the number of bits available. For example:
- 8-bit binary: maximum is 11111111 = 255 decimal
- 16-bit binary: maximum is 1111111111111111 = 65,535 decimal
- 32-bit binary: maximum is about 4.3 billion decimal

Why do computers use binary?

Computers use binary because:
1. Digital circuits have two stable states (on/off, high/low voltage)
2. It's simple and reliable - less chance of errors
3. Binary logic gates (AND, OR, NOT) are easy to implement in hardware
4. All complex operations can be built from simple binary operations
5. Binary arithmetic is straightforward and efficient for electronic circuits

Common Binary to Decimal Conversions