# Floating-Point Number Representation: Sign Bit, Exponent Field, and Fraction Field (Especially for GATE-Geospatial 2022)

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The numbers which are represented by fixed number of digits in the integer and fractional portions are called **floating points**. Their representation in the computer systems is relatively easy. This is because the computer knows clearly the location of the fractional point and hence can manipulate the number easily.

In floating-point representation technique, any number is expressed in terms of its magnitude and range, expressed as (where b is the base, in case decimal , for binary ) . Examples of representing decimal numbers in floating point are shown here.

### Example

Here, is called the mantissa and or is called the exponent.

The aim of floating point representation is show how many numbers before or after the decimal point.

### A Floating-Point Number is Represented by the Triple Parts

**S** is the **Sign bit** (0 is positive and 1 is negative)

- Representation is called sign and magnitude

**E** is the **Exponent field** (signed)

- Very large numbers have large positive exponents
- Very small close-to-zero numbers have negative exponents
- More bits in exponent field increases range of values

**F** is the **Fraction field** (fraction after binary point)

- More bits in fraction field improves the precision of FP numbers

Value of a floating-point number