Question

Which of the following is the correct representation of a floating point number X?

(a) 2^E

(b) M.2^E(1/2<M<1)

(c) 2M.2^E(1/2<M<1)

(d) None of the mentioned

The question was asked in a national level competition.

This intriguing question originated from Representation of Numbers topic in chapter Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

The correct option is (b) M.2^E(1/2<M<1)

The explanation is: The binary floating point representation commonly used in practice, consists of a mantissa M, which is the fractional part of the number and falls in the range 1/2<M<1, multiplied by the exponential factor 2^E, where the exponent E is either a negative or positive integer. Hence a number X is represented as X= M.2^E(1/2<M<1).