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**Representation of Real Number:**

Binary representation of 41.6875 is 101001.1011

Therefore any real number can be converted to binary number system

There are **two schemes** to represent real number :

- Fixed-point representation
- Floating-point representation

**Fixed-point representation:**

Binary representation of 41.6875 is 101001.1011

To store this number, we have to store **two information,**

-- the part before decimal point and

-- the part after decimal point. This is known as fixed-point representation where the position of decimal point is fixed and number of bits before and after decimal point are also predefined.

If we use 16 bits before decimal point and 8 bits after decimal point, in signed magnitude form, the range is

One bit is required for sign information, so the total size of the number is 25 bits

( 1(sign) + 16(before decimal point) + 8(after decimal point) ).

**Floating-point representation:**

In this representation, numbers are represented by a mantissa comprising the significant digits and an exponent part of Radix R. The format is:

Numbers are often normalized, such that the decimal point is placed to the right of the ** first non zero digit.**

For example, the decimal number,

5236 is equivqlent to 5.236 * 10^{3}

To store this number in floating point representation, we store 5236 in mantissa part and 3 in exponent part.

**IEEE standard floating point format:**

IEEE has proposed two standard for representing floating-point number:

- Single precision
- Double precision

S: sign bit: 0 denoted + and 1 denotes - E: 8-bit excess -27 exponent M: 23-bit mantissa | S: sign bit: 0 denoted + and 1 denotes - E: 11-bit excess -1023 exponent M: 52-bit mantissa |

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