Question 1
a) Determine the value of base x if (211)x = (6A)16 [5 marks]
Please check the example that is available in Chapter2-Part 1. You can chose the method that you feel comfortable with.
b) Convert the followings: [3+3=6 marks]
i) 0xBAD into a decimal number
0x means based 16. Its converting (BAD)16 to decimal number.
ii) 58810 into a 3-base number
Many examples are available in lecture slides.
c) Given a (very) tiny computer that has a word size of 6 bits, what are the smallest negative numbers and the largest positive numbers that this computer can represent in each of the following representations? [3 +3 = 6 marks]
i) One's complement
ii) Two's complement
Please consider to work on sign magnitude first to get 1's complement. Please check the questions are available in Chapter 2-Part2.
Question 2.
a) Consider the following logic diagram of a combinational circuit where A, B, and C are inputs and Q is the output. Three 2-input AND gates and two 2-input OR gates are used in the circuit. It is possible to reduce some of the logic gates without changing the functionality of the circuit. Such component reduction results in higher operating speed (less delay time from input signal transition to output signal transition), less power consumption, less cost, and greater reliability. Construct a logic diagram of a circuit which does have the same function output with only two logic gates (instead of five). Please show the steps. [8 marks]
This question is similar to Example 9 in Chapter 9-Part 1. You need to find the expression , simplify it, and then re-design the efficient circuit. You can use one othe simulator that is available in (Week4-5/Logic Design Simulator) folder to draw the circuit.
b) 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. [5 marks]