5. (2 pts) What would the number 2317.6875 ten be in IEEE 754 single precision f

Question

5. (2 pts) What would the number 2317.6875 ten be in IEEE 754 single precision floating point format. You need to follow the following steps: a). Write the above number in binary. (before normalizing it) b). Write the above number in the normalized format. c). Compute the biased exponent, and write it in binary. d). Write its IEEE 754 single precision floating point format in binary, then in hex. 6. (2 pts) What would the number -386.359375 ten be in IEEE 754 single precision floating point format. You need to follow the following steps: a). Write the above number in binary. (before normalizing it) b). Write above number in the normalized format. c). Compute the biased exponent, and write it in binary. d). Write its IEEE 754 single precision floating point format in binary, then in hex. Please explain how to do it! I want to make sure my answer is right and the process of how I am finding the answer is correct! Thank you :)

Explanation / Answer

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-386.359375

this is a negative number, so the sign bit is 1

386 base 10 in binary is 110000010, I assume you know how to do this. let me know if you don't

so now we have to change .359375 to binary

multiply by 2 .359375 * 2 = .71875

the digit to the left of the decimal point, becomes the first digit to the right of the decimal point.

so far we have .359375 base 10 = .0 base 2

do this again

.71875 * 2 =1.4375

the digit to the left of the decimal point, becomes the next digit right of the decimal point.

so we have .359375 base 10 = .01 base 2

do it again after dropping the 1, left of the decimal point

.4375 * 2= 0.875, so we now have .010 base 2

again

.875 * 2 = 1.75 so we now have .0101 base 2

again

,75 * 2 = 1.5 so we now have .01011 base 2

again .5 * 2 =1.0

so .359375 base 10 = .010111 base 2

so the binary number we are starting with is -110000010.010111

using the rules of scientific notation we can change this to (I'm going to ignore the - for a while)

1.10000010010111 x 2^8

so the exponent is 8, to normalize this we add 127 to 8 8+127=135, so the exponent is 135.

135 in binary is 10000111 --this is 8 bits so we don't have to add leading 0's

the fraction part, also called the significand is 1.10000010010111 but we drop the 1 to the left of the decimal (every signifand will be 1.) and get 10000010010111 we will add 0's to the end to make it 23 bits

so now we have

sign bit 1

exponent 10000111

significand 10000010010111

putting it together we get

11000011110000010010111000000000 base 2 = -386.359375 base 10

which in hex is C3C12E00

1100 0011 1100 0001 0010 1110 0000 0000

C 3 C 1 2 E 0 0

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