Q Advanced Binary Tool

Binary Fixed-Point Converter

Convert fixed-point binary numbers to decimal or encode decimal values as fixed-point binary. Configure integer bits, fractional bits, signed or unsigned representation, and rounding behavior.

✓ Binary ↔ Decimal ✓ Signed Two’s Complement ✓ Unsigned Mode ✓ Custom Fraction Bits ✓ Quantization Details

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Fixed-Point Conversion

● Ready

Binary Fixed-Point Value

You may enter a binary point, or enter raw bits and define the fractional-bit count below.

Decimal Value

The decimal value will be quantized to the selected fixed-point format.

Integer Bits

In signed mode, this count includes the sign bit.

Fractional Bits

Each fractional bit contributes a negative power of two.

Representation

Rounding Mode

Total Width 8 bits

Scale 2^-4

Resolution 0.0625

Format UQ4.4

Enter a value and choose the fixed-point format.

✓ Fixed-Point Conversion Result

Decimal Value

Raw Bits –

Fixed-Point –

Scaled Integer –

Resolution –

Minimum –

Maximum –

Quantized Value –

Quantization Error –

Conversion Breakdown

What Is a Binary Fixed-Point Number?

A binary fixed-point number stores a real value using a fixed number of bits for the integer portion and a fixed number of bits for the fractional portion. Unlike floating-point numbers, the binary point stays at a predetermined position.

For the fixed-point value: 101.101 the place values are: 1 × 2² + 0 × 2¹ + 1 × 2⁰ + 1 × 2⁻¹ + 0 × 2⁻² + 1 × 2⁻³ Therefore: 4 + 1 + 0.5 + 0.125 = 5.625

How Fixed-Point Binary Conversion Works

Integer Bits

Bits to the left of the fixed binary point represent whole-number powers of two. In signed mode, the most significant bit is also the two’s-complement sign bit.

Fractional Bits

Bits to the right represent powers such as 2⁻¹, 2⁻², 2⁻³ and so on. More fractional bits provide finer resolution.

Scaling

A value with F fractional bits uses a scale factor of 2^F. The stored integer is divided by that scale to obtain the real value.

Quantization

Decimal values may not fit the available fractional precision exactly, so they are rounded or truncated to the nearest representable fixed-point value.

Unsigned Fixed-Point Formula

For an unsigned binary word with F fractional bits:

Real Value = Stored Integer / 2^F Example: Raw bits = 01011010 Fraction bits = 4 Stored integer = 90 90 / 16 = 5.625

Signed Two’s-Complement Fixed-Point

Signed fixed-point values commonly use two’s-complement representation. The most significant bit determines whether the stored scaled integer is non-negative or negative.

8-bit signed fixed point with 4 fractional bits: 11000100 Unsigned stored value: 196 Convert from two’s complement: 196 – 256 = -60 Apply scale: -60 / 16 = -3.75

Fixed-Point Resolution

Resolution is the smallest difference between adjacent representable values. It depends entirely on the number of fractional bits.

Fraction Bits	Resolution	Formula
0	1	2⁰
2	0.25	2⁻²
4	0.0625	2⁻⁴
8	0.00390625	2⁻⁸
16	0.0000152587890625	2⁻¹⁶

Fixed-Point Range

The available numeric range depends on total width, fractional bits and whether the format is signed or unsigned.

Unsigned

Minimum is 0. Maximum is (2^N - 1) / 2^F.

Signed

Minimum is -2^(N-1) / 2^F and maximum is (2^(N-1)-1) / 2^F.

Fixed-Point vs Floating-Point

Feature	Fixed Point	Floating Point
Binary point	Fixed position	Moves using exponent
Hardware	Often simpler	More complex
Range	Limited	Very large
Precision	Predictable	Varies with magnitude
Common use	DSP, embedded systems	General scientific computing

Common Uses of Binary Fixed-Point

Embedded Systems

Processors without fast floating-point hardware can use scaled integer arithmetic.

Digital Signal Processing

Fixed-point formats are widely used for filters, audio, communications and real-time DSP.

FPGA & Digital Logic

Fixed-width binary arithmetic maps efficiently to hardware registers and arithmetic units.

Control Systems

Predictable precision and deterministic arithmetic can be valuable in real-time control applications.

Important Fixed-Point Considerations

Important: this converter treats the selected Integer Bits + Fractional Bits as the total storage width. When signed mode is selected, the integer-bit count includes the sign bit. Decimal-to-binary conversion may introduce quantization error because only multiples of 2^-F can be represented.

Related BinaryCon Tools

Binary Fixed-Point Converter FAQs

What is fixed-point binary?

Fixed-point binary uses a predetermined number of integer and fractional bits, so the position of the binary point does not move.

How do I convert fixed-point binary to decimal?

Interpret the raw bit pattern as an integer and divide it by 2^F, where F is the number of fractional bits.

What does Q4.4 mean?

It generally describes a fixed-point format with four integer-related bits and four fractional bits. Exact Q-format naming conventions may differ on whether the sign bit is included, so this converter explicitly shows its bit assumptions.

What is the resolution with 4 fractional bits?

The resolution is 2^-4 = 0.0625.

How are negative fixed-point values represented?

This converter uses two’s complement when Signed mode is selected.

Does decimal-to-fixed-point conversion always preserve the exact value?

No. If the decimal value is not an exact multiple of the format resolution, it must be quantized according to the selected rounding mode.

What is quantization error?

Quantization error is the difference between the original decimal input and the nearest or otherwise selected representable fixed-point value.

What happens if the decimal value exceeds the fixed-point range?

The converter reports an out-of-range error rather than silently wrapping or saturating the value.

Is fixed-point the same as floating-point?

No. Fixed-point keeps the binary point at a constant location, while floating-point uses an exponent to represent a much wider range of magnitudes.

Where is fixed-point arithmetic commonly used?

It is common in embedded systems, DSP, FPGA designs, control systems and applications where predictable precision or lower hardware complexity is useful.