Number system reference

Binary (base 2): digits 0–1. Used in digital logic and CPU instructions.
Octal (base 8): digits 0–7. Used in Unix file permissions.
Decimal (base 10): digits 0–9. The everyday number system.
Hexadecimal (base 16): digits 0–9 and A–F. Used in memory addresses, colours, and byte representations.

When you need number base conversion

Programmers encounter number bases constantly. Binary (base-2) is the native language of CPUs. Hexadecimal (base-16) compactly represents binary: each hex digit represents exactly 4 binary bits, making it easy to read memory addresses, colour values, and byte sequences. Octal (base-8) was common in early Unix systems for file permissions (chmod 755).

Binary (base-2) — only 0 and 1, used in CPU operations, bit manipulation, and logical flags
Octal (base-8) — digits 0-7, used for Unix file permissions (e.g. chmod 755 = 111 101 101 in binary)
Decimal (base-10) — everyday numbers, 10 digits 0-9
Hexadecimal (base-16) — digits 0-9 then A-F, used for memory addresses, colours (#FF5733), and byte values

Frequently Asked Questions

About the Number Base Converter

What it does

Converts integers between decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). All four representations update simultaneously as you type in any field.

Why different bases?

Binary is the native language of computers. Hexadecimal is used in programming, colour codes, and memory addresses because it compactly represents binary data — each hex digit maps to exactly 4 binary bits.

Decimal (base 10) — digits 0–9; everyday counting system
Binary (base 2) — digits 0–1; the foundation of all digital computing
Octal (base 8) — digits 0–7; used in Unix/Linux file permissions
Hexadecimal (base 16) — digits 0–9 and A–F; used in colours, memory, and programming

What is binary (base 2)?

Binary is a number system that uses only two digits: 0 and 1. It is the foundation of all digital computing because transistors can be in two states: off (0) or on (1). The decimal number 42 is 101010 in binary.

What is hexadecimal (base 16)?

Hexadecimal uses 16 symbols: 0–9 and A–F (where A=10, B=11, C=12, D=13, E=14, F=15). It is widely used in programming, HTML colour codes, and memory addresses because it compactly represents binary data — one hex digit represents exactly 4 binary bits.

What is octal (base 8)?

Octal uses digits 0–7. It was historically used in computing because it maps cleanly to groups of 3 binary bits. It is still used in Unix/Linux file permissions, where permissions are represented as 3-digit octal numbers like 755 or 644.

How do I convert binary to decimal manually?

Write out the binary digits from right to left. Each position has a value of 2 to the power of its position (starting at 0). Multiply each digit by its position value and sum. Example: 1011 = (1x8) + (0x4) + (1x2) + (1x1) = 8+0+2+1 = 11 in decimal.

How do I convert hexadecimal to binary?

Each hex digit represents exactly 4 binary bits. Replace each hex character with its 4-bit binary equivalent: 0=0000, 1=0001, ..., 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. Example: 3F = 0011 1111. This works in reverse too: group binary digits in fours and convert each group to hex.