S/U Binary Interpretation

Signed Unsigned Binary Converter

Convert and compare signed two’s-complement and unsigned interpretations of the same binary value. Work with 8-bit, 16-bit, 32-bit and 64-bit values and view binary, hexadecimal and decimal results.

Signed Binary Unsigned Binary Two’s Complement 8 / 16 / 32 / 64 Bit Binary Hex

Signed / Unsigned Interpreter Two’s Complement

Word Size

Input Format

Input Value Enter up to 8 binary bits. Leading zeros are automatically added.

Binary Interpretation Result

–

Fixed-Width Binary –

Hexadecimal –

Unsigned Decimal –

Signed Decimal –

Word Size –

Sign Bit –

Signed State –

Magnitude –

Interpretation Analysis

Signed vs Unsigned Binary

The same fixed-width binary pattern can represent different decimal values depending on whether it is interpreted as unsigned or signed two’s complement.

8-bit binary:
11110010

Unsigned:
242

Signed two’s complement:
-14

Unsigned Binary Interpretation

In an unsigned binary value, every bit contributes a non-negative power of two. All bit patterns therefore represent zero or positive numbers.

8-bit unsigned range:
00000000 = 0
11111111 = 255

Signed Two’s-Complement Interpretation

For signed two’s-complement values, the most significant bit acts as the sign bit. A leading 0 represents a non-negative number, while a leading 1 represents a negative number.

8-bit:

01111111 = +127
10000000 = -128
11111111 = -1

How a Negative Binary Value Is Decoded

When the sign bit is 1, the magnitude can be found by inverting the bits and adding one.

11110010

Invert:
00001101

Add 1:
00001110

Magnitude:
14

Signed value:
-14

Signed and Unsigned Ranges

Width	Unsigned Range	Signed Range
8-bit	0 to 255	-128 to 127
16-bit	0 to 65,535	-32,768 to 32,767
32-bit	0 to 4,294,967,295	-2,147,483,648 to 2,147,483,647
64-bit	0 to 18,446,744,073,709,551,615	-9,223,372,036,854,775,808 to 9,223,372,036,854,775,807

Same Bits, Different Meaning

8-bit Binary	Unsigned	Signed
00000000	0	0
00000001	1	1
01111111	127	127
10000000	128	-128
11110010	242	-14
11111111	255	-1

Important Signed / Unsigned Notes

Important: changing the interpretation does not change the underlying bits.

The signed result uses two’s-complement interpretation.

The most significant bit is the sign bit only when the value is interpreted as signed.

A sign bit of 0 produces the same numeric result under both signed and unsigned interpretation.

A sign bit of 1 produces different signed and unsigned decimal values.

The selected word size is essential because signed interpretation depends on the fixed bit width.

Signed Unsigned Binary Converter FAQs

What is signed binary?

Signed binary uses a representation such as two’s complement to represent both negative and positive values.

What is unsigned binary?

Unsigned binary represents only zero and positive integer values.

Can the same binary value mean two numbers?

Yes. For example, 11111111 is 255 unsigned but -1 when interpreted as an 8-bit signed two’s-complement number.

What is the sign bit?

The most significant bit is the sign bit in a signed two’s-complement representation.

What does a sign bit of 1 mean?

In two’s complement it means the represented signed value is negative.

Does signed-to-unsigned conversion change the bits?

No. This calculator compares the different numeric interpretations of the same fixed-width bit pattern.

Why does word size matter?

The same visible digits can have a different signed interpretation depending on how many total bits belong to the value.

Does the calculator support 64-bit values?

Yes. It supports fixed-width 8-bit, 16-bit, 32-bit and 64-bit values.