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(a) Convert the number 30.12510 into binary. [2 marks] (b) Calculate the value of the expression (11012 + 348 + F0516) ¸ 2 and express the result in binary-coded decimal. [4 marks] (c) Using the laws of boolean algebra, transform the expression
into a sum of products in the simplest form possible. Identify the laws used. [5 marks] (d) Find the simplified sum-of-product and product-of-sum forms of the function F(A, B, C, D) = Õ (0, 5, 10, 15) using a Karnaugh map. [4 marks]
(e)Find the prime implicants of the expression
å (m1, m2, m3, m8, m9) using the Quine-McCluskey method. [5 marks] (f) Draw a block diagram showing the connections on a 2 x 1 multiplexor, and give the truth table describing its behavior. Hence, show how to implement exclusive-or and exclusive-nor (that is, equality) using just two 2 x 1 mulitplexors each. [6 marks] (g) Give the excitation tables for an SR and a JK flip-flop, and show how to convert an SR flip-flop into a JK flip-flop. [4 marks) |
