What is the binary representation of the decimal number 2975

What is the binary representation of the decimal number 29.75 assuming the IEE 754 single
precision format?

Solution

Single precision (32 bits):

                Sign * 2^exponent * mantissa

Binary number of 29.75 is 11101.11

                                             1.110111 * 2^4

Sign Bit

Bit 31

Exponent Field

Bits 30 - 23

Significand

Bits 22 - 0

Sign Bit:-

For positive number sign bit=0

Exponent Field:

           Decimal value of exponent field and exponent

                                      =127+ exponential

                                      =127+4

                                      =131

                                      =10000011 (Binary Number)

Significand:-

                         = 11011100000000000000000

So binary representation is:

0

10000011

11011100000000000000000

=0 10000011 11011100000000000000000

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