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.

What is the Powers of Two Reference Table?

Reference table of powers of two from 2^0 up to 2^256, showing each value in decimal and hexadecimal with binary-prefix labels (KiB, MiB, GiB). Exact BigInt values you can copy for bit masks, buffer sizes, and limits. It runs free in your browser on Gera Tools, with nothing uploaded.

Powers of Two Reference Table

Name: Powers of Two Reference Table
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

Why powers of two appear in programming

Every data type in a binary computer is defined by its bit width, and bit widths are powers of two. A few values show up constantly:

Exponent	Decimal	Common meaning
2^7	128	Max positive value in signed 8-bit int
2^8	256	Total values in a byte (0–255)
2^10	1 024	1 KiB — smallest named binary unit
2^16	65 536	Max unsigned 16-bit integer; port number range
2^24	16 777 216	16M distinct colours in 24-bit RGB
2^31	2 147 483 648	Max positive signed 32-bit integer
2^32	4 294 967 296	Total unsigned 32-bit values; IPv4 address space
2^53	9 007 199 254 740 992	MAX_SAFE_INTEGER in JavaScript (float64 precision limit)
2^64	~1.84×10^19	Max unsigned 64-bit integer

Binary vs decimal prefixes: the source of the confusion

Hard drive manufacturers measure storage in SI (decimal) units: 1 TB = 10^12 bytes. Operating systems measure in binary units: 1 TiB = 2^40 bytes ≈ 1.0995 × 10^12 bytes. The gap grows with scale:

1 GB (advertised) = 1,000,000,000 bytes
1 GiB (OS reports) = 1,073,741,824 bytes ≈ 7.4% more

A drive labelled “1 TB” shows up as “931.3 GB” in Windows File Explorer, which is reporting in GiB using the GB label. This discrepancy is entirely due to the binary vs decimal prefix convention, not missing storage.

Reading powers of two in hexadecimal

Powers of two are exceptionally clean in hex because each additional factor of 16 (2^4) appends exactly one zero:

2^4  = 0x10
2^8  = 0x100
2^12 = 0x1000
2^16 = 0x10000
2^32 = 0x100000000

Bit masks are easy to spot: 0xFF is 2^8 - 1 (8 bits set), 0xFFFF is 2^16 - 1, and so on. This makes the hex column useful for quickly deriving and checking bitmask values in code.

Cryptographic exponents

For RSA keys and cryptographic key spaces, the meaningful values lie at 2^128 (common AES key size), 2^192, and 2^256 (SHA-256 output space). These numbers are enormous — 2^128 is roughly 3.4 × 10^38 — and are the reason brute-forcing a well-chosen key is computationally infeasible even with vast hardware. This table renders them exactly using BigInt arithmetic rather than truncating to floating-point approximations.