Integer ranges and powers of two

The exact limits of every fixed-width integer type from 8 to 64 bits, the values of 2⁶³ and 2⁶⁴ that define the 64-bit boundaries, and a full table of powers of two from 2⁰ to 2⁶⁴ in decimal and hexadecimal. Every number on this page is computed at build time with arbitrary-precision arithmetic.

Signed and unsigned ranges by bit width

With n bits there are exactly 2ⁿ distinct patterns; an unsigned type uses all of them for 0 to 2ⁿ−1. A signed type stores negatives in two's complement, spending half the patterns on −2ⁿ⁻¹ … −1, which leaves 0 … 2ⁿ⁻¹−1 for the non-negative side — so the signed maximum is 2ⁿ⁻¹−1 and the minimum is −2ⁿ⁻¹.

2⁶³ and 2⁶⁴: the 64-bit limits

These five values come up constantly in overflow checks, database column types and "why is my counter negative" bugs:

• 2⁶³ = 9 223 372 036 854 775 808 = 0x8000000000000000 — one past the largest signed 64-bit value.
• 2⁶³ − 1 = 9 223 372 036 854 775 807 = 0x7FFFFFFFFFFFFFFF — int64 max.
• −2⁶³ = −9 223 372 036 854 775 808 — int64 min; its 64-bit two's complement pattern is 0x8000000000000000.
• 2⁶⁴ = 18 446 744 073 709 551 616 = 0x10000000000000000 — needs 65 bits, so it does not fit in any 64-bit type.
• 2⁶⁴ − 1 = 18 446 744 073 709 551 615 = 0xFFFFFFFFFFFFFFFF — uint64 max; the same pattern reads as −1 in int64.

Powers of two from 2⁰ to 2⁶⁴

Each row is linkable by exponent, for example /reference/integer-ranges/#2-63.

Overflow: what happens past the limit

Fixed-width arithmetic is modular: in unsigned 8-bit, 255 + 1 wraps to 0, and in signed 8-bit, 127 + 1 wraps to −128, because the carry out of the top bit is simply discarded. What your language does about it varies — C leaves signed overflow undefined, Java wraps silently, Swift traps at runtime, and Rust panics in debug builds but wraps in release. The two's complement calculator lets you see the wrapped bit pattern for any width, and the two's complement guide explains why the range is asymmetric in the first place.

Related tools and guides

• Two's complement calculator — signed and unsigned readings of any 8- to 64-bit pattern.
• Two's complement explained — sign bits, −1 as all ones, overflow and sign extension.
• Hex calculator — 64-bit arithmetic with overflow detection.
• Hex to decimal table 0x00–0xFF — every byte value with binary and octal.