Boolean Algebra and Circuit Design

Read the required material on Boolean Algebra and circuit design in the Background Information, and complete the problems below. You can locate additional material on the Web (Google "Boolean algebra”, "logic circuits" and "logic gates." if you need further explanations.

1. Convert the following binary numbers to their decimal equivalents

a. 1101

b. 0011

c. 11100111

d. 10101011

2. Convert the following decimal numbers to their binary, octal, and hexadecimal equivalents

a. 16

b. 32

c. 48

d. 80

3. Do the following work and answer the following questions:

a. Explain the relationship between an AND gate and a NAND gate in terms of Boolean Algebra and draw truth tables for both types of gate

b. Explain the relationship between an OR gate and a NOR gate in terms of Boolean Algebra and draw truth tables for both types of gate

4. In the following problems, use 0 to stand for False and 1 to stand for True. Indicate whether the answer is true or false

a. Jack is a boy AND Jill is a girl

b. Jack is NOT a girl

c. Jack is a boy OR Jill is a boy

d. Jack is NOT a boy AND Jill is NOT a boy

e. Jack is a boy OR Jill is NOT a boy

5. Fill in the following truth tables