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Chapter 3: Q40E (page 241)

Question: Based on your answer to 3.38 and 3.39, is

Short Answer

Expert verified

Based on the answers of 3.38 and 3.39, the given equations are not equal

Step by step solution

01

Determine the floating-point multiplication.

The biased exponents of two numbers will be added as the first step of the floating-point multiplication. Then, the significands will be multiplied to get the product. Check the product for normalization, if the necessary product will be normalized by shifting right and incrementing the exponent. Then it will be checked for overflow or underflow. If no underflow or overflow occurs, the product will be rounded off. Finally, the sign of the products will be assigned.

02

 Step 2: Determine whether the equations are equal.

The given equation is ,

Based on the answer of 3.38 and 3.39,

Converting the values into decimal values, we have


Since the values are different, it is clear that the two sides of the equation are not equal.

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Most popular questions from this chapter

IEEE 754-2008 contains a half precision that is only 16 bits wide. The left most bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. A hidden 1 is assumed. Write down the bit pattern to represent -1.5625×10-1assuming a version of this format, which uses an excess-16 format to store the exponent. Comment on how the range and accuracy of this 16-bit floating point format compares to the single precision IEEE 754 standard.

Calculate by hand 8.625×101divided by -4.875×100. Show all the steps necessary to achieve your answer. Assume there is a guard, a round bit, and a sticky bit, and use them if necessary. Write the final answer in both the 16-bit floating point format described in Exercise 3.27 and in decimal and compare the decimal result to that which you get if you use a calculator.

Using a table similar to that shown in Figure 3.6, Calculate the product of the hexadecimal unsigned 8-bit integers 62 and 12 using the hardware described in Figure 3.5. You should show the contents of each register on each step.

Calculate the time necessary to perform a multiply using the approach given in Figure 3.3 and 3.4 if an integer is 8 bits wide and each step of the operation takes 4-time units. Assume that in step 1a an addition is always performed -either the multiplicand will be added, or a zero will be. Also assume that the registers have already been initialized (you are just counting how long it takes to do the multiplication loop itself). If this is being done in hardware, the shifts of the multiplicand and multiplier can be done simultaneously. If this is being done in software, they will have to be done one after the other. Solve for each case.

What do you get if you add -1/4 to itself 4 times? What is -1/4×4? Are they the same? What should they be?

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