Integer Range Calculator
Calculate signed and unsigned limits for any register width from 1 to 128 bits. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.
Enter register bit width.
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Integer Range Calculator?
The Integer Range Calculator provides exact minimum, maximum, and total state capacities for both signed (Two’s Complement) and unsigned integers for any bit width.
How Does It Work?
Computes signed range [-2^(n-1), 2^(n-1) - 1] and unsigned range [0, 2^n - 1] using arbitrary-precision arithmetic.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- Total unique states is always 2^n.
Practical Applications in Engineering
- Database column type selection (TINYINT, SMALLINT, INT, BIGINT).
- Firmware register allocation.
Common Mistakes to Avoid
- Caution: Assuming signed ranges are symmetric around zero.
Frequently Asked Questions
What is the range of a 64-bit integer?
Signed: -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807. Unsigned: 0 to 18,446,744,073,709,551,615.
Related Tools
View All Number Representation Tools →Signed Number Calculator
Evaluate signed integers across 8, 16, 32, and 64-bit Two’s Complement representations.
Two's Complement Range Calculator
Calculate the asymmetric signed range [-2^(n-1) to +2^(n-1)-1] for any bit width n.
32-bit Number Range Calculator
Analyze 32-bit dword limits: signed ±2.14 billion and unsigned 0 to 4.29 billion.