Free Tool Overflow Underflow BigInt Exact

Integer Overflow Detector

Check whether an integer fits inside a signed or unsigned binary width. Detect positive overflow, negative underflow, valid values, exact boundaries, required bit width, binary representation, and hexadecimal output for standard or custom integer sizes.

✓ Signed + unsigned

✓ 1–1024 bits

✓ Required width

✓ Exact arithmetic

Example · signed 8-bit

Valid range -128 … 127

→

Input 128 Overflow

Integer Boundary Checker

RANGE TEST

Decimal integer Exact whole numbers only

Bit width

Integer type

Overflow analysis

Positive Overflow OUT OF RANGE

128 does not fit in signed 8-bit two’s-complement range.

Input value 128

Type Signed

Width 8 bits

Boundary distance 1

Minimum bits needed 9 bits

Minimum valid value -128

↔

Maximum valid value 127

Binary representation Not representable at selected width

Hex representation Not representable at selected width

Overview

What Is Integer Overflow?

Integer overflow occurs when a value lies outside the numeric range that can be represented by a fixed-width integer type.

Every fixed-width integer has a minimum and maximum value. Once a result exceeds one of those boundaries, it cannot be represented using the selected number of bits without changing the value or using a different representation.

Signed and unsigned integers have different limits. An 8-bit signed two’s-complement integer ranges from −128 to 127, while an 8-bit unsigned integer ranges from 0 to 255.

Overflow Value exceeds the maximum

Underflow Value is below the minimum

Fits Value lies inside the valid range

Exact check BigInt avoids precision loss

Detection Method

How to Detect Integer Overflow

Choose the bit width Determine whether the target is 8-bit, 16-bit, 32-bit, 64-bit, or another width.

Choose signed or unsigned interpretation The valid boundaries are different for the two integer types.

Calculate the valid range Signed uses −2^(n−1) through 2^(n−1)−1. Unsigned uses 0 through 2^n−1.

Compare the integer with the boundaries A value above the maximum overflows; a value below the minimum underflows.

Signed Overflow

Signed Integer Overflow Example

Does 128 fit in signed 8-bit? Overflow

Signed 8-bit range: -128 to 127 Input: 128 Maximum: 127 128 > 127 Result: Positive overflow Minimum width needed: 9 signed bits

Negative Boundary

Signed Integer Underflow Example

Does -129 fit in signed 8-bit? Underflow

Signed 8-bit range: -128 to 127 Input: -129 Minimum: -128 -129 < -128 Result: Negative underflow Minimum width needed: 9 signed bits

Unsigned Overflow

Unsigned Integer Overflow Example

Does 256 fit in unsigned 8-bit? Overflow

Unsigned 8-bit range: 0 to 255 Input: 256 Maximum: 255 256 > 255 Result: Positive overflow Minimum width needed: 9 unsigned bits

Standard Limits

Common Integer Overflow Boundaries

Type	Bits	Minimum	Maximum
int8	8	-128	127
uint8	8	0	255
int16	16	-32,768	32,767
uint16	16	0	65,535
int32	32	-2,147,483,648	2,147,483,647
uint32	32	0	4,294,967,295
int64	64	-9,223,372,036,854,775,808	9,223,372,036,854,775,807
uint64	64	0	18,446,744,073,709,551,615

Signed vs Unsigned

Why Signed and Unsigned Overflow Differ

Signed integer

Two’s complement reserves part of the available bit patterns for negative values. An n-bit signed integer ranges from −2^(n−1) to 2^(n−1)−1.

Unsigned integer

Every bit contributes to a nonnegative magnitude, producing a range from 0 to 2^n−1.

Decimal 200 overflows an 8-bit signed integer but fits perfectly inside an 8-bit unsigned integer. The selected interpretation therefore matters.

Required Width

How Many Bits Are Needed to Store an Integer?

When a value does not fit the selected width, the calculator determines the smallest wider integer representation capable of storing it.

Value	Unsigned minimum bits	Signed minimum bits
0	1	1
127	7	8
128	8	9
255	8	9
256	9	10
-128	Not unsigned	8
-129	Not unsigned	9

Arithmetic

Integer Overflow in Addition and Multiplication

Overflow often appears after arithmetic rather than from a literal input. Even when both operands fit individually, their result may exceed the available integer range.

Signed 8-bit addition Arithmetic overflow

100 + 50 = 150 Signed 8-bit range: -128 to 127 150 > 127 Therefore: 150 cannot be represented as signed int8.

The same principle applies to subtraction, multiplication, shifts, counters, accumulators, and conversions from wider types.

Wraparound

Does Integer Overflow Always Wrap Around?

No. Overflow behavior depends on the numeric type and execution environment. Some fixed-width unsigned arithmetic is defined modulo a power of two, while signed behavior may differ across programming languages and runtimes.

Hardware may expose overflow flags, some languages may throw exceptions in checked contexts, some operations may wrap, and other environments may use arbitrary-precision integers instead of overflowing.

This calculator detects whether the mathematical integer lies inside or outside the requested range. It does not assume a particular language’s post-overflow behavior.

Binary Representation

Binary and Hex Output for Values That Fit

When the input fits the selected width, the tool displays its fixed-width binary and hexadecimal representation.

Negative signed values are encoded using their n-bit two’s-complement bit pattern. For example, decimal −1 in signed 8-bit form is 11111111, or hexadecimal FF.

-5 as signed 8-bit Fits

Decimal: -5 Signed width: 8 bits Binary: 11111011 Hex: FB Range: -128 to 127 Status: Fits

Practical Uses

Where Integer Overflow Detection Is Useful

Programming Validate casts and numeric conversions

Embedded Check registers and sensor fields

Protocols Validate binary field limits

Databases Check integer column capacity

Type conversion

Before converting a 32-bit value to 16 bits, checking the destination range can prevent silent data loss or unexpected results.

Protocol validation

A packet field may allow only 12 signed bits or 24 unsigned bits. Detecting range violations helps identify malformed or incorrectly decoded data.

Embedded systems

Hardware registers and sensors often use strict fixed-width integers. Checking limits is important when scaling measurements or combining raw values.

Common Mistakes

Integer Overflow Mistakes to Avoid

Checking only positive overflow

Signed integers also have a lower boundary. A value can fail because it is too negative as well as too positive.

Using unsigned limits for signed data

The 8-bit unsigned maximum is 255, but the 8-bit signed maximum is only 127.

Assuming a value fits because its operands fit

Arithmetic results may require more bits than either original operand.

Using floating-point numbers for very large integers

Ordinary JavaScript Number values cannot exactly represent all 64-bit integers. This detector uses BigInt for exact integer comparisons.

FAQ

Integer Overflow Detector FAQs

Common questions about integer overflow, underflow, signed and unsigned ranges, required bit width, binary limits, and fixed-width arithmetic.

Integer overflow occurs when a value is greater than the maximum value representable by the selected fixed-width integer type.

In this calculator, integer underflow means a mathematical integer is below the minimum representable value of the selected integer type.

Yes. Signed int8 ends at 127, so decimal 128 requires at least 9 signed bits.

Yes. Unsigned 8-bit values range from 0 through 255.

No. Signed 8-bit reaches only −128, so −129 is below the minimum.

Calculate the valid range for the selected signedness and verify that the integer lies between the minimum and maximum inclusive.

A two’s-complement signed n-bit integer ranges from −2^(n−1) through 2^(n−1)−1.

An unsigned n-bit integer ranges from 0 through 2^n−1.

Yes. For example, 100 and 50 both fit in signed 8-bit, but their sum 150 does not.

No. Overflow handling depends on the language, runtime, numeric type, compiler, and processor behavior.

Yes. It reports the minimum signed or unsigned width required to hold the entered integer exactly.

Yes. BigInt is used for the calculations, allowing exact checks for the supported widths up to 1024 bits.