Two's Complement Range Calculator
Calculate the asymmetric signed range [-2^(n-1) to +2^(n-1)-1] for any bit width n. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.
Enter bit width.
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Two's Complement Range Calculator?
The Two's Complement Range Calculator computes the exact valid range of signed integers for any register width n, highlighting why the negative limit is 1 larger in magnitude than the positive limit.
How Does It Work?
Computes Min = -2^(n-1) and Max = 2^(n-1) - 1 using ECMAScript BigInt.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- The range is asymmetric due to zero being included in the non-negative space.
Practical Applications in Engineering
- Preventing integer overflow bugs.
- Compiler optimization of range checks.
Common Mistakes to Avoid
- Caution: Assuming the range extends to +2^(n-1).
Frequently Asked Questions
Why is there no +128 in an 8-bit Two’s Complement signed byte?
Because positive numbers start at 0, leaving 127 positive slots. Value 10000000 is allocated to -128.
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