The following bits represent an IEEE 754 single precision floating point númber

Question

The following bits represent an IEEE 754 single precision floating point númber FLOAT: 10111010011000000000000000000000101008 d A. (15 points) Show the bits after the number it represents has been multiplied by 3. the base 10 number 32 B. (15 pts) If the same floating point number (before the multiply by 32) is stored beginning at address 100 on a Little Endian computer, show the number in hexadecimal at the specific memory addresses it uses. Leave blank any addresses it does not use. Fill in ONLY the addresses that the floating point number uses FLOAT: 101110100110 00000000000000000000 100 101 02 03 4 105 106 107 108 109

Explanation / Answer

Solution:

Note: A part is done, please repost others.

The format for IEEE 754 single precision is (32-bits):

sign

Exponent

Mantissa

1 bit

8 bits

23 bits

The given number will be represented as:

sign

Exponent

Mantissa

1

0111 0100

11000000000000000000000

the sign bit is 1 means the number is negative.

The number in normalized format will be

1.11000000000000000000000

Actual Exponent= Exponent - Bias = 116 - 127 = -11

final number will be

1.11000000000000000000000 * 2^-11

In decimal

-1.75 * 2^-11

= -3584

after multiplying by 32

= -114688

This is the final number after multiplying by 32.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

sign

Exponent

Mantissa

1 bit

8 bits

23 bits

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