Answer any 3 of the following questions. Each question carries 10 marks.
1. Convert the numbers 17 and 21 into signed binary numbers $x$ and $y$ using the 2’s complement method (show each step). Find $x+y$ and $x-y$ and verify whether the results are consistent. Do the results mean 2’s-complemented numbers can be added just like ordinary binary numbers?
2. CMOS transistors are used to create logic gates. Draw the circuit diagram of a CMOS NAND gate, create the truth table of the NAND logic and, finally, verify that the CMOS transistor indeed produces outputs entailed by the truth table.
3. Use the rules of Boolean algebra to show that $AB + A(B + C) + B(B + C) = B+AC$. Draw the logic circuits for both expressions and show that the latter is much simpler. Finally, create the truth table of $B+AC$ and show that the Boolean expression can be derived from the truth table.
4. Draw the logic circuit of a full adder and verify (by showing the inputs and output logic levels in the circuit) that the sum $\Sigma = (A\oplus B)\oplus C_i$ and $C_o = AB+(A\oplus B)C_i$ where $A$ and $B$ are the inputs and $C_i$ and $C_o$ are the input and output carries.
5. Draw the logic circuit of a clocked D flip-flop and show the behavior of the input $D$ and outputs $Q$ and $Q'$ for 3 clock pulses using a timing diagram. Assume that the flip-flop is negative-edge-triggered. Verify that the circuit indeed produces results entailed by the timing diagram.