Number Systems Cheat Sheet

Binary, hex, powers of 2, bitwise operators & color codes — quick reference

Decimal ↔ Binary

Pattern	Description	Example
`0`	0000 — Zero, all bits off	`Zero — all bits off`
`1`	0001 — One	`One`
`2`	0010 — Two	`Two`
`4`	0100 — Power of 2 (2²)	`Power of 2 (2²)`
`8`	1000 — Power of 2 (2³)	`Power of 2 (2³)`
`16`	0001 0000 — Power of 2 (2⁴)	`Power of 2 (2⁴)`
`32`	0010 0000 — Power of 2 (2⁵)	`Power of 2 (2⁵)`
`64`	0100 0000 — Power of 2 (2⁶)	`Power of 2 (2⁶)`
`128`	1000 0000 — Max value of signed byte	`Max value of signed byte`
`255`	1111 1111 — Max value of unsigned byte (0xFF)	`Max value of unsigned byte (0xFF)`

Powers of 2

Pattern	Description	Example
`2⁰`	1	`1 bit`
`2¹`	2	`—`
`2²`	4	`—`
`2³`	8	`—`
`2⁴`	16	`—`
`2⁵`	32	`—`
`2⁶`	64	`—`
`2⁷`	128	`—`
`2⁸`	256	`1 byte combinations`
`2¹⁰`	1,024	`1 KB`
`2²⁰`	1,048,576	`1 MB`
`2³⁰`	1,073,741,824	`1 GB`

Hex ↔ Decimal

Pattern	Description	Example
`0x0`	0 — Zero	`Zero`
`0x1–0x9`	1–9 — Same as decimal	`Same as decimal`
`0xA`	10	`—`
`0xB`	11	`—`
`0xC`	12	`—`
`0xD`	13	`—`
`0xE`	14	`—`
`0xF`	15 — Max single hex digit	`Max single hex digit`
`0xFF`	255 — Max byte	`Used in colors (#FFFFFF)`
`0x100`	256	`—`
`0x7F`	127 — Max signed byte	`Max signed byte`
`0x80`	128 — Min negative signed byte	`Min negative signed byte`

Number Base Prefixes

Pattern	Description	Example
`0b...`	Binary (base 2)	`0b1010 = 10`
`0o...`	Octal (base 8)	`0o12 = 10`
`(none)`	Decimal (base 10)	`42`
`0x...`	Hexadecimal (base 16)	`0xFF = 255`
`%`	Binary (assembly)	`%1010 = 10`
`h suffix`	Hex (assembly)	`FFh = 255`
`0 prefix`	Octal (C/C++)	`012 = 10`
`#`	Hex (CSS colors)	`#FF5733`

Bitwise Operators

Pattern	Description	Example
`&`	AND — bits both 1 → 1	`0b1100 & 0b1010 = 0b1000`
`\|`	OR — at least one bit 1 → 1	`0b1100 \| 0b1010 = 0b1110`
`^`	XOR — bits differ → 1	`0b1100 ^ 0b1010 = 0b0110`
`~`	NOT — flip all bits	`~0b1010 = 0b0101`
`<<`	Left shift — multiply by 2^n	`1 << 3 = 8`
`>>`	Right shift — divide by 2^n	`16 >> 2 = 4`

Common Hex Color Values

Pattern	Description	Example
`#000000`	Black	`color: #000000`
`#FFFFFF`	White	`background: #FFFFFF`
`#FF0000`	Red	`—`
`#00FF00`	Green (lime)	`—`
`#0000FF`	Blue	`—`
`#FF6600`	Orange	`—`
`#808080`	Gray (50%)	`opacity equivalent`
`#CCCCCC`	Light gray	`borders`
`#333333`	Dark gray	`body text`
`rgba(r,g,b,a)`	Red Green Blue Alpha	`CSS: rgba(255,0,0,0.5)`

Frequently Asked Questions

Hexadecimal (base 16) is used in programming and web development because it compactly represents binary data. Each hex digit maps to exactly 4 binary bits, so a byte (8 bits) needs only 2 hex digits (0xFF = 11111111). Web colors, memory addresses, and byte values are commonly written in hex.

Multiply each binary digit by its positional value (powers of 2) from right to left, then add the results. Example: 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11. Or use our Number Base Converter tool for instant conversion.

A bitwise operation works directly on the binary representation of numbers, processing individual bits. Common uses: checking/setting/clearing flags, fast multiplication/division by powers of 2, masking specific bits, and low-level hardware control.