Question

Question: [10] Write down the binary representation of the decimal number 63.25 assuming the IEEE 754 double precision format.

Short answer

The required result will be

Step-by-step solution

Define the concept.

The decimal number system uses base 10 and the binary number system uses base 2.

For example, “12” is also equivalent to the value of the binary number system “1100”.

In the IEEE 754 double-precision format,

Determine the calculation.

The given number is 63.25.

In the decimal number system, 63.25 is equivalent to the binary number

0100000001001111101000000000000000000000000000000000000000000000

This can be written as in the IEEE 754 double-precision format,

Hence, the sign is not negative, the sign is positive.

In the decimal number system, 253 is equivalent to the binary number 11111101.

Hence, the mantissa = 1111101000000000000000000000000000000000000000000000.

In the binary number system, 10000000100 is equivalent to the decimal number 1028.

Hence, the exponent will be 1028-1023=-5.

Hidden 1 is always present in the format of IEEE 754.

In the IEEE 754 double-precision format,

The given number can be written as

Which is equivalent to the