32bit signed integer values have a range of 2e9 2e9 while 32

32-bit signed integer values have a range of ~[-2e9, 2e9], while 32-bit IEEE754 floating-point values have a range of ~[-3.4e38, 3.4e38]. How is this possible? That is, what must be given up to achieve such a larger range using the same number of bits?

Solution

Hi,

Floating point representation is the most common solution for scientific notation to encode numbers,with a base number and an exponent. IEEE floating point numbers having three components.

They are Sign,Exponent,Mantissa. Mantissa is a fration and an implicit leading digit.

In 32 bit the size of sign component is 1 and size of exponent component is 8 and size of mantissa component is 23. In 64 bit the size of sign,exponent,mantissa are 1,11,52 respectivly.

The size of 32bit signed integer is (2^31)-1 where as 32 bit IEEE754 floating point range is 3.4 x (10^38).

Integers with less than or equal to 6 significantdecimal digits can be converted to IEEE754 floating point value with out loss of precision.some integers upto 9 significant digits can be converted to an IEEE 754 floating point value without loss of precision, but not more than 9 digits can bestored.

Consider an example, the 32 bit integer 2,147,483,647 converts to 2,147,483,650 in IEEE 754 form.