Number System Converter - BIN, OCT, DEC, HEX

Number System Converter - before you calculate

Without converter

Manual division by 2/8/16 - easy to make mistakes
Mix up remainder order in BIN conversion
Forget hex digit values A-F
Waste time on CS assignments

With converter

Type a number, pick a system - done
DEC, BIN, OCT, HEX all at once
Verify manual calculations
Result in a fraction of a second

How does the conversion work?

    DEC (decimal) - digits 0-9, base 10

    BIN (binary) - digits 0-1, base 2

    OCT (octal) - digits 0-7, base 8

    HEX (hexadecimal) - digits 0-9 + A-F, base 16

DEC 42 to BIN: 42 / 2 = 21 r 0, 21 / 2 = 10 r 1, 10 / 2 = 5 r 0, 5 / 2 = 2 r 1, 2 / 2 = 1 r 0, 1 / 2 = 0 r 1. Read from bottom: 101010

DEC 255 to HEX: 255 / 16 = 15 r 15 (F), 15 / 16 = 0 r 15 (F). Result: FF

BIN 11001 to DEC: 1x16 + 1x8 + 0x4 + 0x2 + 1x1 = 25

Conversion table - common values

DEC	BIN	OCT	HEX	IT context
0	0	0	0	NULL, false
10	1010	12	A	-
127	1111111	177	7F	Max signed byte (int8)
255	11111111	377	FF	Max unsigned byte, RGB color channel
1024	10000000000	2000	400	1 KB (kibibyte)
65535	1111111111111111	177777	FFFF	Max uint16, TCP port range

Practical examples

CSS color #FF5733: Split into pairs - FF = 255 (Red), 57 = 87 (Green), 33 = 51 (Blue). So #FF5733 = rgb(255, 87, 51) - an orange-red.
Each hex pair converts to a 0-255 decimal value

Linux chmod 755: Octal 755 = binary 111 101 101 = rwx r-x r-x. Owner gets read+write+execute, group and others get read+execute only.
Each octal digit maps to exactly 3 permission bits

IP address 192.168.1.1: Each octet in decimal. 192 = binary 11000000, 168 = 10101000. The full address in binary: 11000000.10101000.00000001.00000001 (32 bits).
Understanding subnet masks requires binary thinking

Memory address 0x7FFF: Hex 7FFF = decimal 32767 = binary 111111111111111. This is the maximum value of a signed 16-bit integer (int16).
Memory addresses are almost always displayed in hex

ASCII character 'A': Decimal 65 = hex 41 = binary 1000001 = octal 101. Every character in a text file has a numeric code - the converter shows all representations at once.
ASCII table values appear in all four number systems

HEX in CSS colors

Color	HEX	RGB (DEC)	BIN (R channel)
Red	#FF0000	255, 0, 0	11111111
Green	#00FF00	0, 255, 0	00000000
White	#FFFFFF	255, 255, 255	11111111
Teal	#14B8A6	20, 184, 166	00010100

FAQ - Frequently Asked Questions

What is binary used for?

Computers operate on bits (0 and 1) - it is the only thing a processor understands. Every operation, text, image is ultimately a sequence of zeros and ones. 8 bits = 1 byte = a number from 0 to 255.

Why do programmers use hexadecimal?

HEX is a shorthand for binary - 1 hex digit = 4 bits. A byte (8 bits) is exactly 2 hex digits. Instead of writing 11111111 you write FF. That is why CSS colors (#FF0000), MAC addresses and memory dumps use hex notation.

How do I convert BIN to DEC manually?

Multiply each digit by its corresponding power of 2 (from right: 1, 2, 4, 8, 16...) and sum. For example, 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 13.

What do the letters A-F mean in hex?

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. The hexadecimal system needs 16 digits but we only have 10 (0-9), so it adds letters A through F for values 10-15.

When is the octal system used?

Mainly in Linux/Unix for file permissions (chmod). 755 = rwxr-xr-x, 644 = rw-r--r--. Each octal digit represents 3 bits, so 3 digits = 9 permission bits (owner/group/others).

How does the CSS color #FF5733 translate to RGB?

Split into pairs: FF = 255 (R), 57 = 87 (G), 33 = 51 (B). So #FF5733 = rgb(255, 87, 51) - an orange-red tone. The converter will turn each hex pair into its decimal equivalent.

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Ready-made calculations

The most searched variants of this calculator. Each link opens it with the value already filled in, ready to calculate.