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FORDHAM UNIVERSITY CSLU 3593

Fordham College Lincoln Center Computer Organization

Dept. of Computer and Info. Science Spring, 2005

Fordham College Lincoln Center Computer Organization

Dept. of Computer and Info. Science Spring, 2005

Homework Assignment 1

**Due date:** January 31

In addition to the basic laws we discussed on pages B-4 and B-5, there
are two important theorems, called DeMorgan's theorems:

**B.1**- [10] §B.2 Prove DeMorgan's Laws by constructing a
truth table. Show intermediate steps.
**B.2**- [15] §B.2 Prove that the following two equations for the
function are equivalent, by using DeMorgan's
laws and the axioms shown on page B-6.

**B.4**- [10] §B.2 One logic function that is used for a variety of
purposes (including within adders and to compute parity) is
*exclusive OR.*The output of a two-input exclusive OR function is true only if exactly one of the inputs is true. Show the truth table for a two-input exclusive OR function and implement this function using AND gates, OR gates, and inverters. **B.4a**- [10] §B.2 Show that the exclusive OR is
associative. That is,

where denotes the excusive-OR operation.*Hint:*the proof can be done by constructing a truth table for each side of the equation. **B.5**- [15] §B.2 Prove that the NOR gate is universal by
showing how to build the AND, OR, and NOT functions using only
two-input NOR gates.
**B.5a**- [15] §§B.2,B.3 Using a diagram in the same
style as the one in Figure B.3.5, show how to implement a full-adder
using a PLA.

Robert Moniot 2005-01-24