Convert between binary, decimal, octal, and hexadecimal. Perform binary arithmetic and bitwise operations (AND, OR, XOR, NOT).
Binary
1010
Common binary conversions and operations
Valid characters: 0-1
Binary (Base 2)
1010
Decimal (Base 10)
10
Octal (Base 8)
12
Hexadecimal (Base 16)
A
| Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Power of 2 | 2^7 | 2^6 | 2^5 | 2^4 | 2^3 | 2^2 | 2^1 | 2^0 |
| Decimal Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Example: 11001010 = 128 + 64 + 8 + 2 = 202
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 4 | 100 | 4 | 4 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 100 | 1100100 | 144 | 64 |
| 128 | 10000000 | 200 | 80 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
Test your understanding of binary conversions and operations
Practice with 6 problems to test your understanding.
Binary
1010
To convert binary to decimal, multiply each binary digit (0 or 1) by its positional power of 2 (right to left: 1, 2, 4, 8, 16...) and sum the results. For example, binary 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 13 decimal. To convert decimal to binary, repeatedly divide by 2 and read remainders bottom-to-top.
Binary is a base-2 number system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, making it the fundamental language of computers and digital electronics. Binary arithmetic and conversions are essential for programming, computer science, and understanding how digital systems process information.
To convert binary to decimal, multiply each binary digit (0 or 1) by its positional power of 2 (right to left: 1, 2, 4, 8, 16...) and sum the results. For example, binary 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 13 decimal. To convert decimal to binary, repeatedly divide by 2 and read remainders bottom-to-top.
Binary is a base-2 number system using only 0 and 1. Each position represents a power of 2. For example, 1011 in binary = 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal. Computers use binary because electronic circuits have two states: on (1) and off (0).
Multiply each binary digit by its positional power of 2 (right to left: 1, 2, 4, 8, 16...) and sum the results. Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 8 + 4 + 0 + 1 = 13.
Repeatedly divide by 2 and collect remainders from bottom to top. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Reading remainders upward: 1101.
Bitwise operations compare bits position by position. AND: both must be 1 to get 1. OR: either can be 1 to get 1. XOR: exactly one must be 1 to get 1. NOT: flips each bit. These are fundamental to computer logic and programming.
Hexadecimal (hex) is base-16 using digits 0-9 and letters A-F (10-15). It's compact for representing binary (4 binary digits = 1 hex digit). Used for colors (#FF0000 = red), memory addresses, and programming. 255₁₀ = FF₁₆ = 11111111₂.
Last updated: 2025-01-15
Binary
1010