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Chapter 3: Q2E (page 237)

Question 3.2 [5] What is 5ED4 - 07A4 when these values represent signed 16- bit hexadecimal numbers stored in sign-magnitude format? The result should be written in hexadecimal. Show your work.

Short Answer

Expert verified

The required result will be 5730.

Step by step solution

01

Define the concept.

The hexadecimal number system uses base 16 where the decimal number system uses base 10 and the binary number system uses base 2.

For example, “A” is equivalent to the value of decimal number system “10” and that is also equivalent to the value of binary number system “1010”.

The given two numbers haven’t the sign bit. Hence the outcome will be as same as for the unsigned format.

02

Determine the calculation.

Given, the two values 5ED4, and 07A4 are represented in unsigned 16-bit hexadecimal numbers.

5ED4 is equivalent to the value of binary number system 0101 1110 1101 0100 and 07A4 is equivalent to the value of binary number system 0000 0111 1010 0100.

Both given two hexadecimal numbers haven’t the sign bit.

Hence,

For the subtraction,

0101 0111 0011 0000 is equivalent to the value of hexadecimal number system 5730.

Hence,

So, the required result is 5730 which is in hexadecimal.

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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.

Question: 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.

Write down the bit pattern in the fraction of value 1/3 assuming a floating-point format that uses binary numbers in the fraction. Assume there are 24 bits, and you do not need to normalize the value of 1/3. Is this representation exact?

As discussed in the text, one possible performance enhancement is to do a shift and add instead of actual multiplication. Since 9×6, for example, can be written 2×2×2+1×6 , we can calculate9×6 by shifting 6 to the left 3 times and then adding 6 to that result. Show the best way to calculate 0×33×0×55 using shifts and adds/subtracts. Assume both inputs are 8 bit unsigned integers.

Question : 3.28 [20] The Hewlett-Packard 2114, 2115, and 2116 used a format with the left most 16 bits being the fraction stored in two’s complement format, followed by another 16-bit field which had the left most 8 bits as an extension of the fraction (making the fraction 24 bits long), and the rightmost 8 bits representing the exponent. However, in an interesting twist, the exponent was stored in sign-magnitude format with the sign bit on the far right! Write down the bit pattern to represent assuming this format. No hidden 1 is used. Comment on how the range and accuracy of this 32-bit pattern compares to the single precision IEEE 754 standards.

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