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# Assessment item 3 Assessment Item 3- Assignment 1 Value: 15% Due date: 21-Dec-2012 Return date: 11-Jan-2013 Submission method options Alternative...

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Assessment item 3 Assessment Item 3- Assignment 1 Value: 15% Due date: 21-Dec-2012 Return date: 11-Jan-2013 Submission method options Alternative submission method Task Task Answer the following questions. 1. Briefly explain any two breakthroughs in the history of computing. [4 marks] 2. Represent the following decimal numbers in binary using 8-bit signed magnitude, one's complement and two's complement: [3 marks] –129 3. Using a "word" of 3 bits, list all of the possible signed binary numbers and their decimal equivalents that are representable in: [3 marks] a. Signed magnitude b. One's complement c. Two's complement 4. If the floating-point number representation on a certain system has a sign bit, a 3-bit exponent and a 4-bit significand, a. What is the largest positive and the smallest positive number that can be stored on this system if the storage is normalized? (Assume no bits are implied, there is no biasing, exponents use two's complement notation, and exponents of all zeros and all ones are allowed.) [3 marks] b. What bias should be used in the exponent if we prefer all exponents to be non-negative? Why would you choose this bias? [2 marks] 5. Is the following distributive law valid or invalid? Prove your answer. [3 marks] x XOR (y AND z) = (x XOR y) AND (x XOR z) False. One method of proof uses a truth table. A more challenging approach using identities employs the relation: a XOR b = ab' + a'b 6. Using the basic identities of Boolean algebra, show that: xy + x'z + yz = xy + x' z [3 marks] 7. Little Susie is trying to train her new puppy. She is trying to figure out when the puppy should get a dog biscuit as a reward. She has concluded the following: a. Give the puppy a biscuit if it sits and wiggles but does not bark. b. Give the puppy a biscuit if it barks and wiggles but does not sit. c. Give the puppy a biscuit if it sits but does not wiggle or bark. d. Give the puppy a biscuit if it sits, wiggles and barks. e. Don’t give the puppy a treat otherwise.
Use the following: S: Sit (0 for not sitting; 1 for sitting) W: Wiggles (0 for not wiggling; 1 for wiggling) B: Barking (0 for not barking; 1 for barking) F: Biscuit function (0, don’t give the puppy a biscuit; 1, give the puppy a biscuit) Construct a truth table and find the minimized Boolean function to implement the logic telling Susie when to give her dog a biscuit. [6 marks] 8. Suppose that a 2M x 16 main memory is built using 256K × 8 RAM chips and memory is word-addressable. [5 marks] a. How many RAM chips are necessary? b. How many RAM chips are there per memory word? c. How many address bits are needed for each RAM chip? d. How many banks will this memory have? e. How many address bits are needed for all of memory? 9. Consider the MARIE program below. a. List the hexadecimal code for each instruction. [4 marks] b. Draw the symbol table. [2 marks] c. What is the value stored in the AC when the program terminates? [2 marks] Hex Addr Label Instruction 100 Start, LOAD A 101 ADD B 102 STORE D 103 CLEAR 104 OUTPUT 105 ADDI D 106 STORE B 107 HALT 108 A, HEX 00FC 109 B, DEC 14 10A C, HEX 0108 10B D, HEX 0000 Rationale This assignment has been designed to allow students to test and demonstrate their ability to: o define and appropriately use information technology terms describe the components of a computer system o describe the characteristics and representations of data, and interpret and compare data in different representations; o decipher assembly code language o calculate the internal structure of computer component (memory).
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