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Question 2 Ā Data Representation in Computers [20 marks]

(a) Using a “word” of 4 bits, list all of the possible signed binary numbers and their decimal equivalents that are representable in: [6 marks]

i) Signed magnitude ii) One’s complement iii) Two’s complement

(b) From the results of the previous question, generalize the range of values (in decimal) that can be represented in any given x number of bits using: [6 marks]

i) Signed magnitude ii) One’s complement iii) Two’s complement

(c) Hex value 0xC29C3480 represents an IEEE-754 single-precision (32 bit) floating-point number. Work out the equivalent decimal number. Show all workings (e.g. converting exponent and mantissa). [8 marks]

Question 3 Ā MARIE Assembly [20 marks]

(a) More registers appear to be a good thing, in terms of reducing the total number of memory accesses a program might require. Given an arithmetic example, Sum=(A+B)-(C+D), support this statement. First, determine the number of memory accesses necessary using MARIE and the two registers for holding memory data values (AC and MBR). Then perform the same arithmetic computation for a processor that has more than three registers to hold memory data values. [8 marks]

(b) Write a MARIE program to calculate some basic statistics on a list of positive numbers. The program will ask users to input the numbers one by one. Assume that all numbers will be in the range 1 to 1000. To terminate the data entry, the user will input any negative number. Once the data entry is complete, the program will show four statistics about the list of numbers: (i) Count, (ii) Minimum value, and (iii) Sum of the numbers.

As an example, if the user enters the following decimal numbers as input (one after the other)

23, 6, 78, 36, 3, 250, 127, 210, Ā5

the program would output the following values as the count, minimum and sum respectively:

8
3
733

Assume that the user will always provide valid numbers as input, that is, do not worry about dealing with invalid input data.