a) Determine the value of base x if (211)x = (6A)16 [5 marks]

Question 1
a)  Determine the value of base x if (211)x = (6A)16       [5 marks]
b) Convert the followings:   [3+3=6 marks]
i) 0xBAD into a decimal number
ii) 58810 into a 3-base number
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
 
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). Show the steps. 


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