32 in binary, octal and hexadecimal

    Convert numbers between decimal (DEC), binary (BIN), octal (OCT) and hexadecimal (HEX). Type a number in any base and get all four representations instantly.

    The decimal number 32 converted into the three bases that matter in computing: binary, octal and hexadecimal. The working is shown rather than just the answer, so this doubles as a way of checking your own conversion by hand. Type a different number below, or switch the input system to convert the other way round.

    Parameters

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    Number system of the input value

    Enter a number in the selected system

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    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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    See also

    Convert 8 From Decimal to Binary, Octal and HexConvert 10 From Decimal to Binary, Octal and HexConvert 12 From Decimal to Binary, Octal and HexConvert 15 From Decimal to Binary, Octal and HexConvert 16 From Decimal to Binary, Octal and HexConvert 64 From Decimal to Binary, Octal and HexConvert 100 From Decimal to Binary, Octal and HexConvert 128 From Decimal to Binary, Octal and HexConvert 255 From Decimal to Binary, Octal and HexConvert 256 From Decimal to Binary, Octal and Hex

    Calculator verified by the LiczGrupa.pl team

    Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.

    Krystian Szyszka

    Reviewed by: Krystian Szyszka

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