UtilVox
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Calculators · Utility

Number Base Converter

Convert numbers between binary, octal, decimal, hexadecimal, and any custom base up to 36.

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Binary (Base 2)
100 0000 0000
Octal (Base 8)
2000
Decimal (Base 10)
1024
Hexadecimal (Base 16)
400

🎛️ Convert to any custom base

SG
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Show successive division steps

Converting decimal 1024 to Base 36 using successive division:

1024 ÷ 36 = 28, Remainder: G
28 ÷ 36 = 0, Remainder: S

Final Result (reversed remainders): SG

Base Digits Reference Table

Base SystemDigits & Symbols Used
Base 2 (Binary)0, 1
Base 8 (Octal)0, 1, 2, 3, 4, 5, 6, 7
Base 10 (Decimal)0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base 16 (Hexadecimal)0-9, A, B, C, D, E, F
Base 36 (Max)0-9, A-Z
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Number Systems Guide

Understanding positional notations and computer mathematics.

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Binary Foundations

Base 2 uses only two digits (0 and 1) to represent information in computer architectures and electrical voltages.

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Compact Hex Notation

Hexadecimal (Base 16) condenses large binary strings into groups of 4 bits, used widely in color codes and memory indexes.

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Positional Logic

Every number system represents values through positional symbols scaled by exponent powers of that system's base.

Frequently Asked Questions

What is the maximum base supported?
UtilVox supports conversions up to Base 36, which fully utilizes numerals 0-9 followed sequentially by letters A-Z.
Can I convert fractions or decimals?
This converter is optimized for integers. Fractional floating-point base support will be integrated in a future revision.
Are results case-sensitive?
No. You can write your values in either uppercase or lowercase. The engine normalizes all inputs to standard alphanumeric keys.

Binary, Decimal, Hex: One Number, Four Outfits

The bases and where you meet them

The same quantity, written in the alphabet each domain prefers:

BaseDigitsHabitat
Binary (2)0–1How hardware actually stores everything
Octal (8)0–7Unix file permissions (chmod 755)
Decimal (10)0–9Humans
Hexadecimal (16)0–9, A–FColors (#7c3aed), memory addresses, MAC addresses

Why hex and binary are best friends

One hex digit is exactly four binary digits — F = 1111, 7 = 0111 — so hex is binary folded into quarters for readability. That's why low-level values everywhere ship as hex: #FF is the byte 11111111 (255), and a permission like 0x1F unpacks mentally digit by digit. Decimal has no such alignment, which is why 255 looks arbitrary while FF looks structural.

Where conversions come up

Reading a color's red channel (#7c = 124), decoding chmod permissions, IP and subnet work (the subnet calculator lives one layer up from this), debugging anything bitwise. For arithmetic in binary rather than conversion, the binary calculator operates directly, and historical numerals — a different base game entirely — convert in the Roman numeral converter.