A machine stores floating point number in a 1123bit word The

A machine stores floating point number in a (1+1+2+3)-bit word. The first bit is for the sign of the number, the second bit is for the sign of the exponent, the next 2 bits are for the exponent, and the final 3 bits are for the mantissa. The largest positive number that can be represented is (Keep 4 decimal places.)

Solution

The relevant bits are in the last (2+3) positions.

The largest positive number corresponds to 11 (the exponent part) and 111 (the mantissa part).

This represents 2³ (11corresponds to 3) and 1/2+1/2² +1/2³

So the required number is 8. +0.5+0.25+0.125= 8.875