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)?