If we use 4 bits IEEE Std 754 1985 similar floating point nu

If we use 4 bits IEEE Std 754 1985 similar floating point number representation We have 1 aign bit 2 bits for Exponent and 1 bits for Fraction. Exponents 00 and 11 are reserved. Bias is 1. Here are questions: a) List all the NONNEGATIVE floating point number representation by using 4 bits IEEE Std 754 1985 similar floating point number representation: b) If we are using the binary number system which use the left most one bit as the sign bit and the last one bit as the fraction part and the rest two bits as the integer part List all the NONNEGATIVE floating point number representation by using this one. c) Compare the difference of 4 bits IEEE Std 1985 similar floating point number representation and the binary number system.

Solution

A. There are 4 bits i.e. 2⁴=16. One bit is used as a sign bit and the last bit is used as fraction bit.

Hence, the numbers with the sign bit as 0 are the NONNEGATIVE floating point numbers.

B.    There are 4 bits, i.e. 2⁴=16. First bit is used as a sign bit and the last bit is used as fraction bit. So, 14 bits are left and in this 7 bits are positive numbers and rest of 7 are negative numbers.

C.    Floating point numbers are represented by scientific notation using base number and exponent. It solves a number of representation problems. There is a sign bit in which 0 denote positive numbers and 1 denotes the negative number. Binary numbers are the numbers that are represented by 2 digits only, i.e. 0 and 1. Floating numbers can be converted into binary form by following example

Floating number 122.75

Binary 1111010.11