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Convert binary numbers (base-2) to decimal numbers (base-10) instantly. Essential for programming, computer science, and digital electronics.
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1111 | 15 |
| 10000 | 16 |
| 11111111 | 255 |
Binary (base-2) is a number system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital electronics. Each digit in a binary number is called a "bit" (binary digit), and computers use binary because electronic circuits can easily represent two states: on (1) or off (0).
To convert binary to decimal, multiply each bit by 2 raised to its position (counting from right to left, starting at 0), then sum all the results.
Example: Convert 1011 to decimal
1 × 2³ = 1 × 8 = 8
0 × 2² = 0 × 4 = 0
1 × 2¹ = 1 × 2 = 2
1 × 2⁰ = 1 × 1 = 1
Total: 8 + 0 + 2 + 1 = 11
Computers use binary because digital circuits can easily represent two states: on (1) or off (0). This makes binary the most reliable and efficient way to store and process information electronically. Transistors, the building blocks of computer chips, work as switches that are either on or off.
With 8 bits, you can represent 256 different values (2⁸ = 256). The range is 0 to 255 in decimal, or 00000000 to 11111111 in binary. This is why a byte (8 bits) is a fundamental unit in computing.
Decimal (base-10) uses ten digits (0-9) and powers of 10 for place values. Binary (base-2) uses only two digits (0-1) and powers of 2 for place values. While decimal is intuitive for humans, binary is more efficient for computers.
A bit is a single binary digit (0 or 1). A byte is a group of 8 bits. Bytes are the standard unit for measuring computer memory and storage. For example, 1 kilobyte (KB) = 1,024 bytes, 1 megabyte (MB) = 1,024 KB.
Yes, computers represent negative numbers using systems like two's complement. In two's complement, the leftmost bit indicates the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude. This allows computers to perform arithmetic operations efficiently.