About Binary Converter
Free binary converter. Convert numbers between binary, decimal, octal, and hexadecimal instantly. Type in any base and see all four numeral systems update side by side.
How to use
- Enter a number in any supported base: binary (base 2), octal (base 8), decimal (base 10), or hexadecimal (base 16). The converter instantly shows the equivalent value in all other bases simultaneously.
- For binary input, enter using only 0s and 1s. For octal, use digits 0-7. For decimal, use digits 0-9. For hexadecimal, use digits 0-9 and letters A-F (case insensitive). The converter validates your input and alerts you to invalid characters.
- View the step-by-step conversion process showing the mathematical method for each base conversion. Understanding the algorithm helps you verify results and perform manual conversions when needed for exams or interviews.
- Use the binary-to-text converter to translate binary strings to readable text (ASCII/UTF-8) and vice versa. The text 'Hello' in binary is 01001000 01100101 01101100 01101100 01101111, where each 8-bit group represents one character.
- Convert large numbers by entering them directly. The converter handles numbers of any practical size, not just single bytes. This is useful for working with IP addresses (32-bit), MAC addresses (48-bit), colour codes (24-bit), and memory addresses.
- Reference the conversion table for commonly used values: binary 1111 = decimal 15 = hex F, binary 11111111 = decimal 255 = hex FF, binary 10000000 = decimal 128 = hex 80. These patterns are fundamental to computer science and networking.
Frequently asked questions
How do I convert binary to decimal?
Multiply each binary digit by its positional power of 2 (from right to left: 1, 2, 4, 8, 16, 32, 64, 128...) and sum the results. For binary 10110101: 1x128 + 0x64 + 1x32 + 1x16 + 0x8 + 1x4 + 0x2 + 1x1 = 128 + 32 + 16 + 4 + 1 = 181 decimal. For quick mental conversion, memorize the powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Each binary 1 in a position adds that power of 2 to the total.
How do I convert decimal to binary?
Repeatedly divide the decimal number by 2 and record the remainders from bottom to top. For 181: 181/2 = 90 remainder 1, 90/2 = 45 remainder 0, 45/2 = 22 remainder 1, 22/2 = 11 remainder 0, 11/2 = 5 remainder 1, 5/2 = 2 remainder 1, 2/2 = 1 remainder 0, 1/2 = 0 remainder 1. Reading remainders bottom to top: 10110101. Alternatively, subtract the largest power of 2 that fits and mark a 1, repeating until you reach 0: 181 - 128 = 53 (1), 53 - 32 = 21 (1), 21 - 16 = 5 (1), 5 - 4 = 1 (1), 1 - 1 = 0 (1) = 10110101.
What is hexadecimal and why is it used?
Hexadecimal (base 16) uses digits 0-9 and letters A-F, where A=10, B=11, C=12, D=13, E=14, F=15. Each hex digit represents exactly 4 binary digits, making hex a compact way to write binary values. Binary 11111111 = hex FF = decimal 255. Hex is used for: colour codes (#FF5733 = RGB 255, 87, 51), memory addresses (0x7FFF0000), MAC addresses (AA:BB:CC:DD:EE:FF), Unicode code points (U+0041 = A), and cryptographic hashes (SHA-256 produces 64 hex characters). Hex is preferred over binary because it is 4x more compact while maintaining a direct relationship to binary.
How does binary relate to computers?
Computers operate using transistors that have two states: on (1) and off (0). All data — text, images, video, programs — is represented as sequences of binary digits (bits). 8 bits = 1 byte, which can represent 256 values (0-255). A character like A is stored as binary 01000001 (decimal 65 in ASCII). A pixel colour might be stored as 24 bits (8 bits each for red, green, blue). A 1 GB file contains 8,589,934,592 individual bits. Understanding binary helps you comprehend file sizes, colour depth, audio quality, and why computers have memory sizes in powers of 2 (256 MB, 512 MB, 1 GB, 2 GB). When you need to transmit binary data through text-only systems (JSON, email), use the
Base64 Encoder to safely encode the binary as ASCII text.
What is octal and where is it used?
Octal (base 8) uses digits 0-7. Each octal digit represents exactly 3 binary digits. Octal was historically popular when computers used word sizes that were multiples of 3 (12-bit, 24-bit, 36-bit machines). Today, its primary use is in Unix/Linux file permissions: chmod 755 sets rwxr-xr-x (owner: read+write+execute, group: read+execute, others: read+execute). Each digit represents a 3-bit permission set: 7 = 111 (rwx), 5 = 101 (r-x), 4 = 100 (r--), 0 = 000 (---). Hexadecimal has largely replaced octal in modern computing.
How do I convert between hex and binary?
Each hex digit maps to exactly 4 binary digits. Memorize the 16 mappings: 0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000, 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. To convert hex to binary, replace each hex digit with its 4-bit equivalent: hex 3F = 0011 1111 = binary 00111111. To convert binary to hex, group bits into sets of 4 from right to left: binary 10110111 = 1011 0111 = hex B7. This direct mapping is why hex is so popular in computing.
What is two's complement for negative numbers?
Two's complement is the standard method computers use to represent negative integers. To find the two's complement of a number: invert all bits (flip 0s to 1s and vice versa), then add 1. For -5 in 8-bit: start with 5 (00000101), invert (11111010), add 1 (11111011). This system allows the same addition circuitry to handle both positive and negative numbers. In an 8-bit system, values range from -128 (10000000) to +127 (01111111). The most significant bit acts as a sign indicator: 0 = positive, 1 = negative. Two's complement is universal in modern computing.
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