Excrciss 4 Answer each of the following questions 1. Assuming single precision I

Question

Excrciss 4 Answer each of the following questions 1. Assuming single precision IEEE 754 format, what decimal number is represented by this word: (15 pts) 2. Write down the binary representation of the decimal mumber -72.50 assuming the IEEE 754 double precision format. Then write in Hex 3. Consider the two 8-bit numbers A-10010101 and B- 01101110 a. Give the decimal equivalent of each number, assuming that the numbers are: b. Add the two binary numbers and interpret the sum, assuming that the numbers are: c. Determine the values of the C, Z, N, and V status bits after the additions. (1) unsigned (2) signed 2's complement. (1) unsigned (2) signed 2's complement 4. Calculate the AMAT for a system with the following properties: LIS hits in 1 cycle with local hit rate 50% L25 hits in 100 cycles with local hit rate 75% L35 hits in 250 cycles with local hit rate 90% Main memory always hits in 1000 cycles

Explanation / Answer

Q1

convert IEEE 754 binary 0011 1110 1001 0000 0000 0000 0000 0000 to decimal

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Step 1: Split the binary into 1+8+23 bit pieces:

00111110100100000000000000000000

0 01111101 00100000000000000000000

Number is positive - the sign bit is zero: 0

The next eight bits are the exponent: 01111101

The next 23 bits are the mantissa: 00100000000000000000000

Step 2: add back the missing hidden digit to the mantissa/significand

00100000000000000000000 --> 1.00100000000000000000000

Step 3: convert the exponent to decimal and subtract 127

binary 01111101 (=64+32+16+8+4+1) = 125 --> 125 - 127 = -2 --> -2**2

Step 4: de-normalize the mantissa/significand (make exponent zero)

1.00100000000000000000000 times 2**-2 --> (must move left 2 places)

--> .0100100000000000000000000 times 2**0

We moved the binary decimal point 2 places to the left, making

the number larger, which allowed us to reduce the exponent by the

same amount (to zero).

Step 5: binary .0100100000000000000000000 -->0.125 in decimal

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