CSE 232
HOMEWORK 2
1. Assume for a particular year that a particular size chip using state-of-the-art technology can contain 1 billion transistors. Assuming Moore’s Law (doubling each 18 months) holds, how many transistors will the same size chip be able to contain in ten years?
2. Evaluate the Boolean equation F = (a AND b) OR c OR d for the given values of variables a, b, c, and d:
a. a=1, b=1, c=1, d=0
b. a=0, b=1, c=1, d=0
c. a=1, b=1, c=0, d=0
d. a=1, b=0, c=1, d=1
3. For the function F = a + a’b + acd + c’:
a. List all the variables.
b. List all the literals.
c. List all the product terms.
4. Convert the function F shown in the truth table in the table to an equation. Don’t minimize the equation.
5. Use algebraic manipulation to minimize the equation obtained in Exercise 4.
6. Determine whether the Boolean functions F = (a + b)’*a and G = a + b’are equivalent, using: (a) algebraic manipulation, and (b) truth tables.
7. Using the combinational design process, create a 4-bit prime number detector. The circuit has four inputs, N3, N2, N1, and N0 that correspond to a 4-bit number (N3 is the most significant bit) and one output P that is 1 when the input is a prime number and that is 0 otherwise.
8. A network router connects multiple computers together and allows them to send messages to each other. If two or more computers send messages simultaneously, the messages “collide” and the messages must be resent. Using the combinational design process of Table 2.5, create a collision detection circuit for a router that connects 4 computers. The circuit has 4 inputs labeled M0 through M3 that are 1 when the corresponding computer is sending a message and 0 otherwise. The circuit has one output labeled C that is 1 when a collision is detected and 0 otherwise.
