Binary, Decimal, Hex & Octal Converter

Binary is a positional number system, meaning the value of each digit depends on its position. In decimal you are used to positions representing ones, tens, hundreds (powers of 10). In binary, positions represent powers of 2: 1, 2, 4, 8, 16, 32 … reading right to left.

Step-by-step method: write out the binary number, label each bit with its positional power of 2 from right to left starting at 2⁰, then multiply each bit (0 or 1) by its power and add up the results.

Example: convert 1101 to decimal

Sum: 8 + 4 + 0 + 1 = 13. So 1101 binary = 13 decimal.

Another example: 11111111 (8 bits all set to 1) 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the maximum value of an unsigned byte.

Shortcut for all-ones patterns: a binary number made of n consecutive 1-bits always equals 2ⁿ − 1. Eight 1s → 2⁸ − 1 = 255. Sixteen 1s → 2¹⁶ − 1 = 65 535.

The standard method is repeated division by 16. Divide the number by 16, record the remainder, then divide the quotient again, repeating until the quotient reaches 0. Remainders of 10–15 are written as A–F. Read the remainders from bottom to top to get the hex value.

Example: convert 764 decimal to hex

Reading the hex digits bottom-up (step 3 → 1): 2FC. Verify: 2 × 16² + 15 × 16 + 12 = 512 + 240 + 12 = 764 ✓

Shortcut for powers of 2: since 256 = 16², any decimal value under 256 fits in exactly two hex digits. 0 → 00, 255 → FF. This is why a single byte is always two hex characters, useful to remember when reading memory dumps or colour codes.

Because 16 = 2⁴, each hex digit expands to exactly 4 binary bits (a nibble), no arithmetic required. Simply replace every hex digit with its 4-bit equivalent from the table below, preserving order.

Example: convert 3E8 hex to binary

Concatenate the groups: 0011 1110 1000. So 3E8 hex = 001111101000 binary = 1000 decimal.

Going the other way (binary → hex) is equally mechanical: group the bits into chunks of 4 from the right, padding with leading zeros if needed, then replace each group with its hex digit. For example, 10110111 → 1011 0111 → B 7 → B7 = 183 decimal.

Why this matters: a 32-bit IPv4 address, a 24-bit RGB colour, a 64-bit pointer: all are commonly written in hex because the nibble boundary makes it trivial to inspect individual bits without any calculation.

Hexadecimal uses 16 symbols: digits 0–9 plus letters A–F, where A = 10, B = 11 … F = 15. Because 16 = 2⁴, every single hex digit maps to exactly 4 binary bits (a nibble). This makes hex a lossless, compact shorthand for binary: two hex digits represent one full byte.

Complete hex ↔ decimal ↔ binary reference:

Example: convert AB hex to binary and decimal A = 1010, B = 1011, so AB hex = 10101011 binary. In decimal: 10 × 16 + 11 = 171.

How to convert decimal to hex: repeatedly divide by 16 and note the remainder. For 255: 255 ÷ 16 = 15 remainder 15 (F); 15 ÷ 16 = 0 remainder 15 (F). Reading remainders bottom-up: FF.

Where hex is used: memory addresses (0x7FFFFFFF), CSS colors (#1A2B3C = R:26 G:43 B:60), SHA-256 hashes (64 hex chars = 256 bits), UTF-8 escape sequences (\xFF), and binary file viewers (hex dumps).

Octal uses eight digits: 0–7. Because 8 = 2³, each octal digit maps to exactly 3 binary bits. This makes octal a compact grouping of binary, similar to hex but less common in modern systems.

Octal ↔ binary mapping:

How to convert decimal to octal: divide repeatedly by 8 and collect remainders. For 255: 255 ÷ 8 = 31 r7; 31 ÷ 8 = 3 r7; 3 ÷ 8 = 0 r3. Reading bottom-up: 377.