1. Determine the decimal value of each of the following unsigned binary numbers:

a. 10011001
b. 01110100
c. 10111111

2. Determine the decimal value of each of the following signed binary numbers displayed in the 2's complement form:

a. 10011001
b. 01110100
c. 10111111

3. Determine the outputs (Cout, Sout) of a full-adder for each of the following inputs:

a. A = 1, B = 0, Cin = 0
b. A = 0, B = 1, Cin = 1
c. A = 0, B = 0, Cin = 1
d. A = 1, B = 1, Cin = 1

4. The circuit below is an attempt to build a half-adder. Will the Cout and Sout function properly? Demonstrate your rationale.

5. Determine the outputs for the circuit shown below. Assume that C0 = 0 for all cases.

6. Derive the Boolean equation for A = B, when A and B are 4-bit numbers.

7. Complete the timing diagram below for a 2-bit adder. (10 points)

8. Answer the following:

8.1. What is the frequency of a periodic waveform with a period of 1.0 µsec?

a. 100 Hz b. 10 kHz c. 100 kHz d. 1 MHz

8.2. How many bits are required to represent decimal numbers from -256 to +255?

a. 6 b. 7 c. 8 d. 9

8.3. What is the largest positive number that can be represented by 10 signed bits?

a. 511 b. 512 c. 1024 d. 2047

9. The full-adder shown below is tested under all input conditions as shown. Is the circuit operating correctly? If not, what is the most likely fault?

10. Using a 4-bit adder/subtractor, carry out the binary operations for 9 - 3 and 3 - 9. What can you conclude about the answers and the carry out bit (C4)?