Answer Happy

Question 2 (32 marks) You are suggested to read the whole question before attempting to answer. Two bit comparison circuit You are going to design a combinational circuit that compares two 2-bit unsigned numbers AAo and BBo to see whether B is greater than A. The circuit has one output Q which is 1 if A <B, and 0 if AB. (a) (3 marks) By considering on how comparison can be done bit-by-bit from the most significant to the least significant, write the equation for Q using A1, A0, B1, and Bo. (b) (4 marks) Draw the schematic diagram of the circuit that directly implements the equation. (c) (4 marks) Show the condensed truth table with inputs A, B1, Ao, Bo, and output Q (note the order of inputs) which shows all entries where Q = 1, with the last entry "Others” for inputs and output Q = 0. Hint: there are four rows in the condensed truth table. (d) (4 marks) Show the truth table with inputs A1, A, B1, and Bo, and use K-map to simplify the design. (e) (2 marks) Draw the simplified circuit of part (d) Four bit comparison circuit You are going to extend the circuit to compare two 4-bit unsigned numbers A3A2A1Ao and B3B2B Bo to see whether B is greater than A. The circuit has one output Q which is 1 if A<B, and 0 if AB. (1) (15 marks) By extending the techniques in earlier parts of this question, show the steps that bring you to draw the circuit schematic of the circuit. There is no need to optimise the circuit.