multiplication in binary using Booth's algorithm

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Display all references. For full credit, all work must be shown; this includes calculations, derivations, proofs, graphs, as well as your arguments and reasoning. Your argumentation and reasoning is important; results without detailed arguments will not result in much credit. This statement means one file, not many, and not in JPEG, MS Word DOC, or any format other than PDF. 1. Compare the number of steps involved in multiplication in binary using Booth's algorithm, regular multiplication, and repeated addition, as well as the approximate number of minor cycles for an IA-32 ISA. Use the following sets of values given as radix decimal numbers, assuming a 16 bit machine. 1.1 10, 100 1.2 -10, 100 1.3 10000, 10000 (Hint: consider if this is possible given the machine you are to use. 1.4 Using regular elementary multiplication as repeated addition, compute in radix binary the product of 0x32 and 0x0F, where 0x is the standard C++ syntax for radix hexadecimal. 1.5 Repeat 1.4 using Booth's algorithm. 2. Consider the two numbers in radix decimal: A = 105 and B = -1037. 2.1 Explicitly convert each decimal number to binary (radix two) in 2s complement 2.2 Explicitly convert each decimal number to hexadecimal (radix sixteen) in 1s complement. 2.3 Using 2s complement integer arithmetic, explicitly find the result A + B in binary. 2.4 Using 2s complement integer arithmetic, explicitly find the result A - B in binary. 2.5 Using 2s complement integer arithmetic, explicitly find the result A/B (long division) in binary. 2.6 Repeat the division in (2.5), but now show the result including any explicit binary fractions, and express the result with the explicit binary point on display. Note that this is not a _oating point encoding, but a theoretical calculation (not necessarily used in any actual physical machine) that shows the explicit fractional part, if any. 3. Consider the real number X := -4056 (not an integer), and the real number Y := 12 (not an integer). 3.1 Encode X in IEEE 754 single precision floating point, showing explicitly your construction. 3.2 Encode Y in IEEE 754 single precision floating point, showing explicitly your construction. 3.3 Explicitly show the steps required in IEEE 754 single precision floating point to form X+ Y. 4. (Design question). In the textbook author's material, it is stated: Experienced programmers know that it's better for a program to crash than to have it produce incorrect, but plausible, results. Comment upon this statement - under what circumstances would you agree with the statement, and under what circumstances (types of applications), if any, would you disagree with the statement? Other than the abnormal exit of a program, what other possibilities might you consider, and why? Please use examples as needed and justify your conclusions; your reasoning is important.

    • 8 years ago
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