Question

Question: 3.22 [10] What decimal number does the bit pattern 0×0C000000 represent if it is a floating point number? Use the IEEE 754 standard.

Short answer

The required result will

Step-by-step solution

Define the concept.

The hexadecimal number system uses base 16 where the decimal number system uses base 10 and the binary number system uses base 2.

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

In the IEEE 754 standard,

Determine the calculation.

The given pattern is 0X0C000000.

0X0C000000 = 0000 1100 0000 0000 0000 0000 0000 0000 [as,“c” in the hexadecimal number system is equal to the 12 in the decimal number system, which is equal to 1100 in the binary number system].

This can be written as,

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

In the binary number system, 00011000 is equal to the 24 in the decimal number system.

And the exponent will be 24-127=-103

And the mantissa = 0 [As, $18x0=0$]

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

In the IEEE 754 standard,

This can be written as