Binary Translator — Text, Decimal & Hex to Binary

Binary is the number system that computers use to represent and process all information. Where decimal uses ten digits (0–9) and hexadecimal uses sixteen (0–9 plus A–F), binary uses just two: 0 and 1. Each 0 or 1 is called a bit. A group of eight bits is a byte, and a byte can represent 256 distinct values — from 00000000 (decimal 0) to 11111111 (decimal 255).

The relationship between binary and decimal is positional. In decimal, each digit position represents a power of 10: the rightmost digit is 10⁰ (ones), the next is 10¹ (tens), then 10² (hundreds). In binary, each position represents a power of 2: the rightmost bit is 2⁰ (1), the next is 2¹ (2), then 2² (4), 2³ (8), and so on. To convert the binary number 10110101 to decimal: (1×128) + (0×64) + (1×32) + (1×16) + (0×8) + (1×4) + (0×2) + (1×1) = 181.

Hexadecimal compresses binary efficiently: four bits map exactly to one hex digit. The binary sequence 1111 is hex F (decimal 15); 0101 is hex 5. An 8-bit byte fits in exactly two hex digits, which is why memory addresses, color values (#FF5733), and network masks are written in hex rather than binary.

Where binary conversion comes up in practice

IP addresses and subnetting. IPv4 addresses are 32-bit binary numbers. The subnet mask 255.255.255.0 in binary is 11111111.11111111.11111111.00000000 — this makes it immediately clear that the first 24 bits identify the network and the last 8 identify the host.

CSS color values. The hex color #3A6FD8 represents three binary bytes: red (00111010), green (01101111), blue (11011000). Developers who write bitwise color operations or debug color channel values work in binary or hex to verify their calculations.

Bitwise operations in programming. Developers use binary when setting, clearing, and toggling individual flags in integers using AND (&), OR (|), XOR (^), and NOT (~) operators. A programmer checking whether bit 3 of a register is set writes out the binary mask to verify the logic.

ASCII and character encoding. The letter 'A' is decimal 65, hex 41, binary 01000001. The null byte is binary 00000000. When debugging encoding issues, reading protocol dumps, or working with raw file formats, binary conversion maps each byte back to a number system that makes the bit pattern visible.

This tool converts between decimal, binary, and hexadecimal — the three number bases used most in computer science, networking, and low-level programming. Choose a mode tab, enter your value, and click Translate to get the result instantly.