Question

on 15 0 out of 1 points Consider a 16 bit floating-point number system. The sign bit is the most significant bit.6 bits are reserved for the used. remaining 9 bits are the mantissa. A bias of 31 is to be Represent +Infinity in binary using the floating-point representation above.

I need all steps with the reason and detail

Thanks

Answer 1

SInce the number system used is a 16-bit binary system(also referred as 16 base 2 format,where 16 represents number of bits used and 2 represents base of the number system:binary)

In general the sign of the number systems will be represented in the Most Significant Bit (MSB)position on the left most position of the number that is represented just like representing an integer

for signed numbers , the value of MSB signifies the positive or negative symbol for the number

MSB=1 means negative

MSB=0 means positive

for the given number system , the number format is like :

1 bit (MSB) for representing the sign +/-

6 bits to represent the value of exponent

9 bits for representing the mantissa

making a total of 16 bits as shown below

IT WAS ALSO MENTIONED THAT THE NUMBER SYSTEM IS SIGNED AND BIASED .This means the value that represents the exponent is an offset from the actual value.this helps higher values to be stored in less number of bits in 2's complement form instead of direct representation of binary values

Here the numbee system uses 6 bit exponent which is capable of representing values from 0- 2⁶ (0 to 31) making a total of 32 values with a maximum bias value : 31

in order to get the true exponent the offset of 15(01111₂) has to be subtracted from the stored exponent.

The stored exponents

(00000)₂ used to represent zero and

(11111)₂ used to represent infinity

are interpreted specially in floating point number system.

since an infinity value cannot be represented numerically with a limited number of bits in the mantissa,all the bits representing the mantissa value remain zeroes

the floating point 16-bit representation of + infinity is shown below:

bits 0-8 = 000000 (mantissa all bits reset)

bits 10-14=111111 (representing special interpretation of value infinity)

bit 15(MSB) = 0 (representing + symbol)