Why do powers of two matter in computing?

Computers store data in bits, so capacities, address ranges, and limits cluster on powers of two. A byte holds 2^8 = 256 values and a 32-bit unsigned integer maxes out at 2^32 - 1, which is why these exact numbers come up constantly.

What are KiB, MiB, and GiB?

They are binary prefixes: 1 KiB = 2^10 = 1024 bytes, 1 MiB = 2^20, and 1 GiB = 2^30. They differ from the decimal SI prefixes (kB = 1000 bytes), and this table marks the round powers where each applies.

How are the large values kept exact?

Values are computed with BigInt, so even 2^256 is shown as its full exact integer. Ordinary floating-point numbers lose precision above 2^53, so a naive table would print wrong digits for large exponents.

How do I read the hexadecimal column?

Powers of two are clean in hex: 2^4 is 0x10, 2^8 is 0x100, and each extra factor of 16 (four bits) adds a trailing zero. This makes hex handy for bit masks and memory offsets.

What is the largest exponent I can list?

You can list up to 2^256. That is far beyond any common machine word size but useful for cryptographic key spaces, where 2^128 and 2^256 describe the number of possible keys.

Powers of Two Reference Table

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Powers of two are the backbone of how computers measure and address everything: memory sizes, integer limits, bit flags, and color depths all land on a power of two. This reference lists 2 raised to each exponent in decimal and hexadecimal, marks the binary-prefix boundaries, and lets you copy any exact value.

How it works

Each row is computed by repeated doubling, starting from 2 to the power 0:

2^0 = 1
2^(n+1) = 2 * (2^n)

The decimal column is the value itself; the hex column is the same number in base 16, where powers of two are especially tidy. Binary prefixes attach at the round exponents — 2^10 is one kibibyte (KiB), 2^20 is one mebibyte (MiB), 2^30 is one gibibyte (GiB), and so on up through PiB, EiB, ZiB, and YiB. Every value uses BigInt, so even 2^256 prints its full 78-digit integer exactly.

Tips and example

An unsigned 8-bit byte holds 2^8 = 256 distinct values (0–255); a 16-bit value holds 2^16 = 65536.
In hex, each factor of 16 shifts by four bits: 2^4 is 0x10, 2^8 is 0x100, 2^12 is 0x1000 — a quick way to sanity-check bit masks.
The gap between binary and decimal prefixes grows: a “1 TB” drive (10^12 bytes) is only about 0.909 TiB (2^40 bytes), which is why advertised and reported sizes differ.

Copy the exact value you need straight into a constant or a comment without retyping a long number.