Number Base Converter: Any Base 2 to 36

This page handles any base from 2 to 36 and writes out the division-and-remainder steps, which is the part worth seeing if you are learning the method rather than just needing the answer. For the four bases you actually meet in programming, the binary, octal, decimal and hex converter shows all four at once and updates as you type.

Number base systems (also called radixes or positional numeral systems) are the foundation of all digital computing. Every computer operates in binary (base 2), while humans work most naturally in decimal (base 10). Converting between bases is a core skill in computer science, electronics, and low-level programming.

This calculator handles the four common bases from the dropdown, and any base from 2 to 36 through the custom field. The ceiling is 36 because the digits run 0 to 9 and then A to Z, and the alphabet stops there. Base 1 is excluded for a different reason: with only one symbol there is no positional notation to speak of.

The four most important bases:

Converting decimal to any base, the repeated division algorithm: Divide the decimal number by the target base, record the remainder, then repeat with the quotient until it reaches 0. Read remainders from bottom to top.

Worked example, decimal 178 to binary (base 2):

• 178 ÷ 2 = 89, remainder 0
• 89 ÷ 2 = 44, remainder 1
• 44 ÷ 2 = 22, remainder 0
• 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
• Read bottom to top: 10110010

Converting from any base to decimal, the positional value method:

Decimal Value = d_n × base^n + d_{n-1} × base^{n-1} + ... + d_1 × base^1 + d_0 × base^0

Worked example, binary 10110010 to decimal: = 1×128 + 0×64 + 1×32 + 1×16 + 0×8 + 0×4 + 1×2 + 0×1 = 128 + 32 + 16 + 2 = 178 ✓

Hexadecimal digit mapping:

Handy cross-reference table:

Real-world applications:

• Web colors: #FF5733 is hex. Red=FF(255), Green=57(87), Blue=33(51)
• IPv4 addresses: 192.168.1.1 in decimal; each octet is one byte (0–255)
• File permissions: chmod 755 in octal = 111 101 101 in binary (rwxr-xr-x)
• ASCII codes: Character ‘A’ = decimal 65 = hex 41 = binary 1000001