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.
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The calculator instantly shows the equivalent in binary, hexadecimal, and octal.
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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
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.
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