Question 1

•Task  1 

a) Determine the value of base x if (211)x = (152)8

b) A computer stores all integers in 8 bits. The computer also uses 2's complement method for representing negative numbers and IEEE 754 single precision representation for storing floating point values. Please show how the following values(in decimal) would be stored in the computer: 

i) -35

ii) -22.625

Task 2. 

a) Express the switching circuit shown in the figure below in binary logic notation:

b) Write Boolean expressions and construct the truth table describing the outputs of the circuit depicted by the following logic diagram: 

c) Using basic Boolean algebra identities for Boolean variables A, B and C, prove that ABC+ ABC' + AB'C + A'BC = AB + AC + BC. Please show all steps and mention the identities used. 

Question 2

[This task requires you to use the MARIE simulator for Question 1. Prior to starting this task, you must ensure that the simulator is running correctly by completing the tutorial provided with the simulator, located under Resources within the Interact site.]

1. Write a MARIE program using a loop that multiplies two non-negative numbers by using repeated addition. For example, to multiply 3 x 6, the program would add 3 six times (e.g. 3 + 3 + 3 + 3 + 3 + 3) or add 6 three times (e.g. 6+6+6). You should write and run the program using MARIE simulator. Also write the code with Address, Instruction, and Comments . 

2. You are designing an instruction set for your computer. All the instructions are of same size (11 bits long). The size of an address field is 4 bits. You have already designed five 2-address instructions and 40 1-address instructions. How many 0-address instructions can still you can fit? Justify your answer. 

3. Write code to implement the expression: A= (B + C) * (D - E) on 3-, 2-, 1- and 0-address machines. In accordance with programming language practice, computing the expression should not change the values of its operands.

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