Number Systems Converter
Convert numbers between binary, octal, decimal, and hexadecimal. Supports integers and shows step-by-step conversion with place values and bit patterns.
Number Systems Converter
BIN
0-1
OCT
0-7
DEC
0-9
HEX
0-F
Binary Representation
Grouped (4-bit nibbles)
1111 1111
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Quick Reference Table (0–255)
| DEC | HEX | OCT | BIN |
|---|---|---|---|
| 0 | 00 | 000 | 00000000 |
| 1 | 01 | 001 | 00000001 |
| 2 | 02 | 002 | 00000010 |
| 3 | 03 | 003 | 00000011 |
| 4 | 04 | 004 | 00000100 |
| 5 | 05 | 005 | 00000101 |
| 6 | 06 | 006 | 00000110 |
| 7 | 07 | 007 | 00000111 |
| 8 | 08 | 010 | 00001000 |
| 9 | 09 | 011 | 00001001 |
| 10 | 0A | 012 | 00001010 |
| 11 | 0B | 013 | 00001011 |
| 12 | 0C | 014 | 00001100 |
| 13 | 0D | 015 | 00001101 |
| 14 | 0E | 016 | 00001110 |
| 15 | 0F | 017 | 00001111 |
| 16 | 10 | 020 | 00010000 |
| 32 | 20 | 040 | 00100000 |
| 48 | 30 | 060 | 00110000 |
| 64 | 40 | 100 | 01000000 |
| 127 | 7F | 177 | 01111111 |
| 128 | 80 | 200 | 10000000 |
| 192 | C0 | 300 | 11000000 |
| 255 | FF | 377 | 11111111 |
How to Use Number Systems Converter
- 1Enter a number in any base: binary (01), octal (0-7), decimal, or hexadecimal (0-F).
- 2See the equivalent value in all other number systems instantly.
- 3View the bit pattern and place value breakdown.
- 4Adjust the number of bits for binary display (8, 16, 32, 64).
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What is a number system?▾
A number system (or numeral system) is a way to represent numbers using a set of symbols and rules. The base (radix) determines how many symbols are used. Binary (base 2): 0, 1 — used by all digital computers. Octal (base 8): 0-7 — used in Unix file permissions (chmod 755). Decimal (base 10): 0-9 — standard human counting system. Hexadecimal (base 16): 0-9, A-F — used in programming, color codes, memory addresses, and more.
How do I convert decimal to binary?▾
Divide repeatedly by 2, record remainders: 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Read remainders bottom to top: 1101. Verification: 1×8 + 1×4 + 0×2 + 1×1 = 8+4+0+1 = 13 ✓. In JavaScript: (13).toString(2) = "1101". For hex: (255).toString(16) = "ff". To parse: parseInt("1101", 2) = 13, parseInt("ff", 16) = 255.
Why do programmers use hexadecimal?▾
Hexadecimal is a compact representation of binary data: 1 hex digit = exactly 4 bits. A byte (8 bits) is 2 hex digits. Examples: 0xFF = 11111111 = 255, 0x1A = 00011010 = 26, 0xDEADBEEF = 32 bits. Memory addresses (0x7fff5fbff800), color codes (#FF6347), UUID (550e8400-e29b-41d4-a716-446655440000), IPv6 (2001:0db8::), file headers (magic bytes: 0x89PNG), network MAC addresses (00:1A:2B:3C:4D:5E).
What are two's complement and signed integers?▾
Two's complement is the standard way to represent negative integers in binary. For an 8-bit integer: 0=00000000, 127=01111111 (positive, MSB=0), -1=11111111, -128=10000000 (negative, MSB=1). To negate: flip all bits, add 1. Example: 5 = 00000101, flip = 11111010, +1 = 11111011 = -5. Advantage: addition/subtraction works the same for positive and negative numbers, no separate negative-zero. JavaScript's bitwise operators work on 32-bit signed integers.
How are colors represented in hexadecimal?▾
CSS color hex codes use 6 hex digits: #RRGGBB. Each pair is a byte (0-255). #FF0000 = R:255 G:0 B:0 = red. #00FF00 = green. #0000FF = blue. #FFFFFF = white. #000000 = black. 3-digit shorthand: #RGB = #RRGGBB when pairs repeat (#FAB = #FFAABB). 8-digit with alpha: #RRGGBBAA (#FF000080 = 50% transparent red). JavaScript: parseInt("FF", 16) = 255. The hex color space has 16,777,216 possible colors (256^3).