1 - Express the following numbers in IEEE 32-bit floating point format 3 8 -15 -

Question

1 - Express the following numbers in IEEE 32-bit floating point format

3

8

-15

-1.75

128

-1/64

2 - The following numbers use the IEEE 32-bit floating point format. Find the equivalent decimal value.

0 01110011 10000000000000000000000

1 01111100 00000000000000000000000

0 11100001 11000000000000000000000

1 10000011 11100000000000000000000

3 - Find one integer that cannot be represented in 24-bit 2’s complement notation. Explain why not. Find one floating point number that cannot be represented in IEEE 32-bit format. Explain why not.

3

8

-15

-1.75

128

-1/64

Explanation / Answer

3 in floating point format 0 10000000 10000000000000000000000

8 in floating point format 0 10000010 00000000000000000000000

-15 in floating point format 1 10000010 11100000000000000000000

-1.75 in floating point format 1 01111111 11000000000000000000000

128 in floating point format 0 100001100 0000000000000000000000

-1/64 in floating point format 1 01111001 00000000000000000000000

0 01110011 10000000000000000000000 decimal number is 0.0003662109375

1 01111100 00000000000000000000000 decimal number is -0.125

0 11100001 11000000000000000000000 decimal number is 5.5459714E29

1 10000011 11100000000000000000000 decimal number is -30.0

Find one integer that cannot be represented in 24-bit 2’s complement notation?

The square root of 1 cannot be converted in 24-bit 2’s
Value of square root of -1 is 1i which is not a decimal a number. Hence we cannot convert into floating point format

0 11111111 00000000000000000000000 floating point number that cannot be represented in IEEE 32-bit format
The values of 0 11111111 00000000000000000000000 = Infinity. Hence it cannot be represented

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