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5 tips for working with number systems

5 min read

2026-02-10

Practical advice for programmers and students: how to quickly translate numbers, remember correspondences and avoid mistakes.

Tips for working with number systems

1. Remember powers of two

Knowing powers of 2 speeds up translations: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. This is a basic programmer skill.

2. Group bits for HEX

Every 4 binary digits = 1 hexadecimal. 1010 1111 = AF. This allows you to translate long binary numbers piece by piece.

3. Octal through triplets of bits

Group the bits by 3: 101 111 = 57 in octal. Handy for Unix permissions.

4. Use prefixes in your code

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`0b1010` - binary in most languages

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`0o12` - octal

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`0xFF` - hexadecimal

5. Check the limits

Maximum for 8 bits: 255 (0xFF), for 16 bits: 65535 (0xFFFF), for 32 bits: 4294967295 (0xFFFFFFFF). Knowing these boundaries helps with debugging.

Bit depthMaximum (DEC)Maximum (HEX)
8 bit255FF
16 bit65 535FFFF
32 bit4 294 967 295FFFFFFFF

See also: Color converter, Data converter

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