Homework 3 Tutorial

• Instructions: Work through the following problems.

1. Determine the decimal value of the following unsigned binary number: 110001

2. Determine the decimal value of the following unsigned binary number: 1111111

3. Determine the decimal value of the following unsigned binary number: 1000000000

4. Determine the value in base 2 of the following base 10 (decimal) number: 64

5. Determine the value in base 2 of the following base 10 (decimal) number: 95

6. Determine the value in base 2 of the following base 10 (decimal) number: 408

7. The value of the expression (A>1) AND (B=C) is true when

a.    A=1,B=5,C=5
b.    A=10,B=5,C=5
c.    A=0,B=5,C=5
d.    A=10,B=4,C=9

8. The value of the expression [(A+B)>C] AND (B<=C) is true when

a.    A=10,B=4,C=9
b.    A=3,B=4,C=3
c.    A=1,B=2,C=3
d.    A=1,B=6,C=3

9. The value of the expression NOT[(A=B) OR (B=C)] is true when

a.    A=1,B=1,C=1
b.    A=1,B=1,C=9
c.    A=1,B=2,C=9
d.    A=1,B=9,C=9

10. The following is a message coded in ASCII using eight bits per symbol. What does it say?

01000011            01101111            01101101            01110000            01110101            01110100

01100101            01110010            01010011            01100011            01101001

01100101            01101110            01011010            01100101

11. Consider the following truth table:

A         B            Output
0          0            1
0          1            0
1          0            0
1          1            1

Which of the following Boolean expressions corresponds to this table?

a.   (~A + ~B) · (A+B)
b.   ~(A + B) · (A+B)
c.    (~A · ~B) + (A·B)
d.    ~(A · B) + (A·B)

12. The odd-parity function has three inputs and one output. The circuit outputs a 1 if and only if an even number (0 or 2) of its inputs are 1. Otherwise, the circuit outputs a 0. Thus the sum of the number of 1 bits in the input and the output is always an odd number. (This circuit is used in error checking. By adding up the number of 1 bits, we can determine whether any single input was accidentally changed. If it was, the total number of 1's will be an even number when we know it should be odd.). Draw a circuit diagram for the odd-parity function.