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Binary to Decimal Tool

Signed Binary to Decimal Converter

Convert signed binary to decimal using two’s complement, one’s complement, or sign-magnitude notation. Enter the bit pattern, choose the signed representation, and see the decimal value with a clear calculation breakdown.

3 signed formats Two’s complement, one’s complement and sign-magnitude.

Automatic sign detection The leading bit is interpreted according to your chosen format.

Step-by-step result See exactly how the negative or positive value is derived.

Flexible bit width Use common patterns such as 4, 8, 16 or 32 bits.

Signed Binary Converter

● LIVE

ENTER SIGNED BINARY

BASE 2

SIGNED FORMAT

DECIMAL RESULT BASE 10

-5

8-bit Two’s Complement

11111011₂ → unsigned 251 → 251 − 256 = -5₁₀

TRY AN EXAMPLE

Input Signed binary bit pattern

Default Two’s complement

Alternative Modes One’s complement + sign-magnitude

Output Signed decimal integer

Example 11111011₂ = −5₁₀ in 8-bit two’s complement

Signed Binary to Decimal Converter

A signed binary number represents both positive and negative integer values. Unlike ordinary unsigned binary, where every bit contributes to a non-negative magnitude, signed binary reserves or interprets the most significant bit in a special way.

This signed binary to decimal converter supports three common signed representations: two’s complement, one’s complement, and sign-magnitude. Choose the representation used by your bit pattern before converting because the same binary digits can have different decimal meanings under different signed systems.

Important: The bit width matters. For example, 11111011 interpreted as an 8-bit two’s-complement value equals −5. The same digits interpreted as an unsigned binary integer equal 251.

What Is Signed Binary?

Unsigned binary represents zero and positive whole numbers. For an unsigned 8-bit value, the range is 0 through 255. Signed binary formats use the available bits differently so that negative numbers can also be represented.

There is no single universal interpretation of the phrase “signed binary.” Several encoding systems exist, although modern computers overwhelmingly use two’s complement for signed integers.

MOST COMMON Two’s Complement

The standard representation used by most modern processors and programming languages for signed integer arithmetic.

HISTORICAL / THEORY One’s Complement

Negative values are produced by flipping every bit of the corresponding positive number.

SIGN + MAGNITUDE Sign-Magnitude

The first bit represents the sign and the remaining bits represent the absolute magnitude.

How Two’s Complement Binary Converts to Decimal

Two’s complement is the most commonly used signed integer representation. If the leading bit is 0, the value is non-negative and can be converted as ordinary binary. If the leading bit is 1, the bit pattern represents a negative number.

For an n-bit negative two’s-complement value:

decimal value = unsigned value − 2ⁿ

For example, interpret 11111011₂ as an 8-bit signed two’s-complement number.

11111011₂ unsigned = 251
bit width = 8
2⁸ = 256

251 − 256 = −5

How One’s Complement Converts to Decimal

In one’s complement, a positive number begins with 0. A negative number begins with 1 and is created by flipping every bit of the positive magnitude.

To decode a negative one’s-complement number, invert all bits and convert the resulting positive binary number to decimal. Then apply a negative sign.

11111010₂

Invert every bit:
00000101₂

00000101₂ = 5₁₀

Therefore: 11111010₂ = −5₁₀ in 8-bit one’s complement.

One’s complement has both a positive zero and a negative zero, which is one reason two’s complement became more practical for general-purpose computer arithmetic.

How Sign-Magnitude Binary Converts to Decimal

Sign-magnitude representation treats the most significant bit as a sign bit. A leading 0 indicates a positive number, while a leading 1 indicates a negative number. All remaining bits give the magnitude.

10000101₂

Sign bit = 1 → negative
Magnitude = 0000101₂ = 5

Result = −5₁₀

Like one’s complement, sign-magnitude has two possible representations of zero: positive zero and negative zero.

Signed Binary Representation Comparison

The same decimal value may have different binary patterns depending on the signed representation being used.

Decimal	8-bit Two’s Complement	8-bit One’s Complement	8-bit Sign-Magnitude
+5	00000101	00000101	00000101
−1	11111111	11111110	10000001
−5	11111011	11111010	10000101
+0	00000000	00000000	00000000
−0	Not separate	11111111	10000000

Signed Binary Ranges by Bit Width

For two’s-complement signed integers, an n-bit value has a range from −2ⁿ⁻¹ through 2ⁿ⁻¹ − 1.

Bit Width	Minimum Signed Value	Maximum Signed Value	Unsigned Range
4-bit	−8	7	0 to 15
8-bit	−128	127	0 to 255
16-bit	−32,768	32,767	0 to 65,535
32-bit	−2,147,483,648	2,147,483,647	0 to 4,294,967,295

How to Use the Signed Binary Converter

Enter the complete binary bit pattern Type the signed binary value using only 0 and 1. Leading zeros are important because they determine the bit width.

Select the signed representation Choose two’s complement, one’s complement, or sign-magnitude according to the format used by your data.

Convert to decimal The calculator checks the sign bit and applies the correct decoding rule.

Review the calculation Use the explanation shown below the result to verify how the signed value was interpreted.

Signed Binary to Decimal Examples

8-BIT TWO’S COMPLEMENT 11111011₂ = −5₁₀


251 − 256 = −5

8-BIT TWO’S COMPLEMENT 11111111₂ = −1₁₀


255 − 256 = −1

8-BIT TWO’S COMPLEMENT 10000000₂ = −128₁₀


128 − 256 = −128

8-BIT TWO’S COMPLEMENT 01111111₂ = 127₁₀


Leading bit is 0 → ordinary binary = 127

ONE’S COMPLEMENT 11111010₂ = −5₁₀


Invert → 00000101₂ → 5 → apply negative sign

SIGN-MAGNITUDE 10000101₂ = −5₁₀


Sign = negative · magnitude 0000101₂ = 5

Why Bit Width Matters in Signed Binary

Signed binary cannot always be interpreted correctly without knowing how many bits belong to the number. The leading bit acts as the sign indicator or has a negative positional meaning, depending on the encoding.

For example, the bit pattern 1111 is −1 in 4-bit two’s complement. The pattern 00001111, however, is +15 in 8-bit two’s complement. Adding leading zeros changes the bit width and therefore can change the signed interpretation.

When working with memory dumps, machine instructions, registers or network data, always preserve the original bit width before interpreting a signed binary value.

What Is Sign Extension?

Sign extension is used when a signed binary number is widened to a larger bit width while preserving its numeric value.

For a positive two’s-complement number, additional zeros are added to the left. For a negative two’s-complement number, additional ones are added to the left.

8-bit −5:
11111011

16-bit sign extension:
1111111111111011

Both represent −5.

Simply adding zeros to the left of a negative signed number would change its meaning, which is why correct sign extension is important.

Where Signed Binary Values Are Used

CPU

Processor Registers CPU registers frequently hold signed integer values in two’s-complement form.

CODE

Programming Signed integer types in common programming environments are generally represented using two’s complement.

DBG

Debugging Raw register or memory values often need to be interpreted as signed decimal numbers.

MCU

Embedded Systems Sensor readings, counters and control values may be stored as signed binary integers.

ASM

Assembly Language Signed arithmetic and conditional operations depend on correct interpretation of bit patterns.

EDU

Computer Science Signed representations are fundamental topics in digital logic and computer architecture.

Common Signed Binary Conversion Mistakes

Treating signed binary as unsigned. A pattern beginning with 1 may represent a negative value rather than a large positive integer.
Ignoring the encoding type. Two’s complement, one’s complement and sign-magnitude do not decode negative values in the same way.
Removing leading zeros or ones. The original bit width can be essential to determining the correct signed value.
Assuming the first bit simply means negative. That description works directly for sign-magnitude, but two’s complement uses a different mathematical interpretation.
Using the wrong range. An 8-bit signed two’s-complement integer ranges from −128 to +127, not −255 to +255.
Confusing signed integers with floating point. IEEE 754 floating-point numbers use separate sign, exponent and fraction fields and must be decoded differently.

Signed Binary to Decimal FAQs

What is signed binary?

Signed binary is a binary representation capable of expressing both positive and negative numbers. Common signed formats include two’s complement, one’s complement and sign-magnitude.

How do I convert signed binary to decimal?

First identify the signed representation and bit width. Then decode the sign according to that format and convert the remaining or transformed binary value to decimal.

What does a leading 1 mean in signed binary?

In common signed representations, a leading 1 normally indicates a negative value. The exact decoding method depends on whether the number uses two’s complement, one’s complement or sign-magnitude.

What is 11111111 in signed decimal?

As an 8-bit two’s-complement value, 11111111₂ equals −1. Under other signed representations, the same pattern can have a different meaning.

What is 10000000 in 8-bit signed binary?

In 8-bit two’s complement, 10000000₂ represents −128, the smallest possible 8-bit signed integer.

What is the range of an 8-bit signed binary number?

For two’s complement, the range is −128 through +127.

Why does signed binary need a bit width?

The most significant bit participates in the signed interpretation. Changing the number of bits can therefore change which bit acts as the sign-related position.

What is the difference between signed and unsigned binary?

Unsigned binary uses all bits to represent a non-negative magnitude. Signed binary reserves or mathematically interprets the highest-order bit so negative numbers can also be represented.

Which signed binary format is most common?

Two’s complement is the dominant signed integer representation in modern computer systems.

What is sign-magnitude binary?

Sign-magnitude uses the most significant bit to indicate the sign and the remaining bits to represent the magnitude.

What is one’s complement binary?

In one’s complement, a negative value is formed by inverting every bit of the corresponding positive binary number.

Does two’s complement have negative zero?

No. Two’s complement has only one representation of zero. One’s complement and sign-magnitude both have separate positive-zero and negative-zero patterns.

Can I convert 16-bit or 32-bit signed binary?

Yes. The calculator derives the bit width directly from the number of bits you enter and applies the selected signed representation.

Is signed binary the same as IEEE 754?

No. Signed integer formats and IEEE 754 floating-point formats are different. IEEE 754 uses separate sign, exponent and significand fields.

Is this signed binary converter free?

Yes. The converter runs directly in the browser and does not require signup.

Convert Signed Binary to Decimal Accurately

Use the converter at the top of this page when you need to interpret a signed binary bit pattern as a decimal integer. Preserve the original bit width, select the correct representation, and review the calculation shown with the result.

For most modern computing tasks, two’s complement is the appropriate choice. One’s complement and sign-magnitude remain useful when studying historical systems, digital logic and alternative signed-number representations.