Free Tool Unsigned Integer 1–1024 Bits Exact BigInt

Unsigned Integer Range Calculator

Calculate the exact minimum and maximum value for any unsigned n-bit integer. Check uint8, uint16, uint32, uint64 or custom widths and inspect total representable values, maximum binary pattern, hexadecimal limit, and the full unsigned range.

✓ Exact maximum

✓ Custom widths

✓ Binary + hex

✓ Local calculation

8-bit unsigned integer range

Minimum 0

↔

Maximum 255

U+

Unsigned Range Calculator

N-BIT RANGE

Bit width 1 to 1024 bits

Unsigned range formula 0 to 2^n − 1

Unsigned integer range

Minimum value 0

↔

Maximum value 255

Bit width 8 bits

Total values 256

Minimum Always 0

Formula 2^8 − 1

Minimum binary 00000000

Maximum binary 11111111

Minimum hex 00

Maximum hex FF

Overview

What Is an Unsigned Integer Range?

An unsigned integer range is the complete set of nonnegative values that can be represented using a fixed number of binary bits.

Unlike signed integers, unsigned integers do not reserve any bit pattern for negative values. Every available bit contributes to the magnitude, so the minimum is always zero and the maximum occurs when every bit is 1.

An n-bit unsigned integer therefore contains exactly 2ⁿ different values ranging from 0 through 2ⁿ − 1.

0 Minimum unsigned value

2ⁿ − 1 Maximum unsigned value

2ⁿ Total representable values

All bits Every bit contributes to magnitude

Formula

Unsigned Integer Range Formula

General n-bit unsigned range Formula

Minimum: 0 Maximum: 2^n – 1 Total representable values: 2^n

For an 8-bit unsigned integer, n = 8. That gives a maximum of 2⁸ − 1 = 255 and a total of 256 possible values.

Method

How to Calculate the Range of an N-Bit Unsigned Integer

Identify the bit width Let n equal the total number of bits in the unsigned integer.

Calculate 2^n This gives the total number of possible bit patterns.

Subtract one for the maximum Since counting starts at zero, the largest value is 2^n − 1.

Minimum remains zero The all-zero bit pattern always represents unsigned zero.

Standard Types

Common Unsigned Integer Ranges

Type	Bits	Maximum	Total values
uint8	8	255	256
uint16	16	65,535	65,536
uint32	32	4,294,967,295	4,294,967,296
uint64	64	18,446,744,073,709,551,615	18,446,744,073,709,551,616

Worked Example

8-Bit Unsigned Integer Range

Calculate the uint8 range 8-bit

Bit width: n = 8 Minimum: 0 Maximum: 2^8 – 1 = 256 – 1 = 255 Unsigned range: 0 to 255 Total values: 256

16-Bit Example

16-Bit Unsigned Integer Range

A 16-bit unsigned integer has 65,536 possible bit patterns and can store values from zero through 65,535.

uint16 range 16-bit

Minimum: 0 Maximum: 2^16 – 1 = 65,535 Total values: 65,536

32-Bit Example

32-Bit Unsigned Integer Range

A 32-bit unsigned integer is commonly used for counters, identifiers, bit masks, addresses, binary formats, protocol fields, and other values that never need to become negative.

uint32 range 32-bit

Minimum: 0 Maximum: 2^32 – 1 = 4,294,967,295 Total values: 4,294,967,296

64-Bit Example

64-Bit Unsigned Integer Range

uint64 range 64-bit

Minimum: 0 Maximum: 2^64 – 1 = 18,446,744,073,709,551,615 Total values: 18,446,744,073,709,551,616

Binary Limits

Minimum and Maximum Unsigned Binary Patterns

The minimum unsigned value contains only zeros. The maximum contains only ones because every available bit contributes its full positional value.

Width	Minimum binary	Maximum binary
4-bit	`0000`	`1111`
8-bit	`00000000`	`11111111`
16-bit	`0000000000000000`	`1111111111111111`
32-bit	`00000000000000000000000000000000`	`11111111111111111111111111111111`

Hex Limits

Unsigned Integer Maximum Values in Hexadecimal

When the width is a multiple of four, every four maximum binary bits become hexadecimal F. This makes unsigned boundaries especially easy to recognize in hexadecimal.

Width	Maximum binary	Maximum hex
8-bit	`11111111`	`FF`
16-bit	`1111111111111111`	`FFFF`
32-bit	32 ones	`FFFFFFFF`
64-bit	64 ones	`FFFFFFFFFFFFFFFF`

Signed vs Unsigned

Unsigned Integer Range vs Signed Integer Range

Unsigned n-bit integer

Uses all bit patterns for values from 0 through 2^n−1.

Signed n-bit integer

Uses two’s complement and ranges from −2^(n−1) through 2^(n−1)−1.

8-bit comparison Signed vs unsigned

Unsigned 8-bit: 0 to 255 Signed 8-bit: -128 to 127 Total patterns in both: 256

The same raw binary pattern can have a different decimal meaning depending on whether the field is interpreted as signed or unsigned.

Custom Widths

Unsigned Ranges for Nonstandard Bit Widths

Hardware fields and packed data structures often use widths other than 8, 16, 32, or 64 bits. The same unsigned formula works for any width.

Bits	Minimum	Maximum
3	0	7
5	0	31
10	0	1,023
12	0	4,095
24	0	16,777,215

Overflow

What Happens Above the Maximum Unsigned Value?

A fixed-width unsigned integer cannot directly represent any value above 2ⁿ − 1. Depending on the environment, arithmetic beyond this limit may wrap modulo 2ⁿ, trap, saturate, or be handled using a wider integer type.

For example, decimal 256 does not fit in an 8-bit unsigned integer because uint8 ends at 255.

Always check the target integer width when parsing external data, performing arithmetic, converting types, or validating protocol fields.

Practical Uses

Where Unsigned Integer Range Calculation Is Useful

Counters Determine maximum counter capacity

Protocols Validate unsigned binary fields

Embedded Check register and sensor ranges

Bit masks Understand all-ones width boundaries

Counters and IDs

Unsigned integers are often ideal for counters, sequence numbers, identifiers, and quantities that never need negative values.

Network and file formats

Binary protocols commonly define fields as unsigned integers with exact widths such as 8, 12, 16, 24, or 32 bits.

Embedded hardware

Registers often contain unsigned measurements or flags. Knowing the width immediately reveals the largest representable value.

Common Mistakes

Unsigned Integer Range Errors to Avoid

Using the signed maximum formula

The signed maximum is 2^(n−1)−1, but unsigned integers can use the full range up to 2^n−1.

Forgetting that zero counts as a value

An n-bit unsigned field contains 2^n values even though its maximum is one less than 2^n.

Treating the highest bit as a sign bit

In an unsigned integer, the most significant bit contributes to magnitude. It is not a sign indicator.

Using ordinary floating-point math for huge limits

Large integer boundaries can exceed the exact-integer capacity of standard JavaScript Number values. This calculator uses BigInt for exact results.

FAQ

Unsigned Integer Range Calculator FAQs

Common questions about unsigned integer limits, bit widths, maximum values, binary patterns, hexadecimal boundaries, and overflow.

The range is from 0 to 2^n−1, with a total of 2^n representable values.

An 8-bit unsigned integer ranges from 0 to 255.

A 16-bit unsigned integer ranges from 0 to 65,535.

A 32-bit unsigned integer ranges from 0 to 4,294,967,295.

A 64-bit unsigned integer ranges from 0 to 18,446,744,073,709,551,615.

There are 2^n different bit patterns, but counting starts at zero, so the largest numeric value is one less than the total number of patterns.

Exactly 2^n values.

A pattern containing 1 in every bit position produces the maximum value.

Unsigned integers represent only nonnegative values, while signed two’s-complement integers divide the available bit patterns between negative and nonnegative values.

Yes. It supports any whole-number width from 1 through 1024 bits.

A 24-bit unsigned integer ranges from 0 to 16,777,215.

Yes. The calculator uses JavaScript BigInt, so large integer boundaries remain exact rather than being rounded by floating-point arithmetic.