## 5.11. Exercises

### Exercises for 5.4 Circuits

1. Create a 1-bit XOR circuit using only AND, OR, and NOT gates. Explicitly show all steps starting from the truth table for XOR, then listing the logical expressions for when XOR is 1, and then translating the expressions into a circuit.

2. List the truth table for the full 1-bit adder circuit with 3 input values (A, B, and CARRY IN), and two output values (SUM and CARRY OUT).

3. Create a 4-bit negation circuit using only basic logic gates (AND, OR, NOT), and a 1-bit adder circuit. Assume that the high-order bit (bit 3) is the sign bit of the two’s complement 4-bit values. Refer to Chapter 4 for details on negation of two’s complement numbers.

4. For the 4-way multiplexer circuit shown in the Control Circuits section, explain why an S input value of 1 results in the multiplexer outputting B’s value.

5. How many selection bits are needed for a 16-way multiplexer? Explain your answer.

6. Draw an RS latch circuit that stores 0. Then, trace through the updates to the circuit to write 1 into it. Use the RS latch figure in the Storage Circuits section, as an example.

7. For the figure of the gated D latch shown in the Storage Circuits section, what input values result in writing 1 into the latch? What inputs result in writing 0 into the latch?

8. Explain why the D input to the gated D latch has no affect on the value stored in the latch when the WE input is 0.