please solve number 1 What would be the IEEE 754 single precision floating point

Question

please solve number 1

What would be the IEEE 754 single precision floating point representation of n = -76543210.9876543210 1234 x 10^18? For explanation, I want you to document the steps you perform, in this order: (1) What is n in decimal fixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 25 bits following the binary point; (3) What is the normalized binary number, written in the form 1.bbbbb...bbb x 2^e, storing 25 bits following the binary point? (4) What are the 23 mantissa bits, after the bits in bit positions -24, -25, ... are eliminated using the round to nearest, ties to even mode; exclude the 1. part which is not stored; (5) What is the biased exponent in decimal and in binary? (6) Write the 32-bits of the number in the order: s e m; and (7) Write the final answer as an 8-hexdigit number.

Explanation / Answer

Solution:

So the number is -765543210.98765432101234 * 1018

we can also write this as -765543210987654321012340000

Now let's cover this into binary

100111100100111110000101

and our floating point representation will be like

1)

-765.54321098765432101234 * 1024

2)

100.111100100111110000101 * 221

3)

1.00111100100111110000101* 223

4)

Mantissa is 00111100100111110000101

5)

Biased exponent is

11011000

6)

11101100 00011110 01001111 10000101

7)

in hexadecimal it will be 0xEC1E4F85

Sign Exponent Mantissa 1 11011000 00111100100111110000101

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