Number Base Converter
Convert numbers between decimal, binary, hexadecimal, and octal instantly.
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How to use this calculator
- 1
Enter a decimal (base 10) number in the input field.
- 2
The calculator instantly shows the equivalent in binary, hexadecimal, and octal.
- 3
For hexadecimal output, letters A–F represent values 10–15.
Frequently asked questions
What is binary?
Binary is base-2 — it uses only the digits 0 and 1. Computers store all data in binary because electronic circuits have two states: on (1) and off (0). The decimal number 10 in binary is 1010.
What is hexadecimal used for?
Hexadecimal (base-16) is widely used in computing to represent binary data more compactly. Each hex digit represents 4 binary bits. It uses digits 0–9 and letters A–F. Colour codes in web design (#FF5733) are hexadecimal.
How do I convert decimal to binary?
Repeatedly divide the decimal number by 2 and record the remainders. Read the remainders from bottom to top. For example, 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → 13 in binary = 1101.
What is octal?
Octal is base-8, using digits 0–7. It was used in early computing as a shorthand for binary groups. Today it is still used in Unix file permissions (chmod 755 means rwxr-xr-x).
What is 255 in binary and hexadecimal?
255 in binary is 11111111 (eight 1s). In hexadecimal it is FF. This is the maximum value for an 8-bit (1-byte) unsigned integer, common in colour codes (RGB values).
Number base conversion explained
How to use the number base
Use this number base to onvert numbers between decimal, binary, hexadecimal, and octal instantly. Enter your values above and get your result in seconds. The tool is free, works on all devices, and keeps your data private — nothing is stored or shared.
How the number base works
The number base converter uses standard formulas used in unit conversion in science, engineering, cooking, and everyday use. Enter your inputs, and the tool calculates the result instantly in your browser. No server-side processing means your data stays on your device. Results update in real time as you change inputs.
Why different number bases exist
Humans use base-10 (decimal) because we have 10 fingers. Computers use base-2 (binary) because circuits have two states. Hexadecimal (base-16) was introduced as a compact way to write binary — each hex digit replaces exactly 4 binary digits. Octal (base-8) was used in early minicomputers.
Quick reference: decimal 0–16
Dec: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | Bin: 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 | Hex: 0 1 2 3 4 5 6 7 8 9 A B C D E F 10.
Practical uses for base conversion
Web colours use hex (#FFFFFF = white, #000000 = black). IP addresses use both decimal (192.168.1.1) and binary internally. Unix permissions use octal. Assembly and low-level programming use all four bases regularly.
Number base: how it works
Unit conversion matters across engineering, science, cooking, and everyday life. This tool applies internationally recognised conversion factors to deliver precise, instant results across all major unit systems — no manual lookup needed.
Who uses this tool?
Scientists, engineers, chefs, and international travellers use this tool daily to bridge the gap between different measurement systems. It eliminates the need to memorise conversion factors or hunt through reference tables.
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