CMSC 311- Computer Organization

Fall 1995 - Assignment #1

Due (at the beginning of class) Thursday, September 14

1. In class we saw that a NOR gate is functionally complete (it can be used to represent the other 7 gates). Show that NAND is functionally complete by showing how each of the other 7 gates can be constructed using one or more NAND gates.

2. Given this circuit:

1. Write out the truth table.
2. Write out the sum of products representation of F(A,B,C).
3. Algebraically simply the following expressions to as few literals as possible:
1. (x + y) (x + y')
2. xyz + x'y + xyz'
3. x + xz + yx + xyz + x'yz
4. y(xz' + ((x' + z)y)')
4. From Mano, problem 1-4.
5. From Mano, problem 1-5.
6. The implication function is one of the 16 possible functions of two Boolean variables. It is written x -> y, and is defined by x -> y = x' + y.
1. Prove or disprove the associativity of this function (does (x -> y ) -> z = x -> (y -> z)).
2. Prove or disprove the communtativity of this function (does x -> y = y -> x).
7. From Mano, problem 1-7.
8. Use Karnaugh maps to find a simplified sum of products representation of the following functions (you need to show the Karnaugh map to receive full credit).
1. F(a,b,c) = (0,1,2,3)
2. F(a,b,c) = abc' + ab'c' + a'bc' + a'bc
3. F(a,b,c,d) = (1,2,4,5,7,8,10,11,13,14)
4. F(a,b,c,d) = a'b'c + ad + bd' + cd' + ac' + a'b'