Information Management

System Architecture

Exercise 1: Basics and Simple Logic

1. What are the main components of any computer? Draw a functional block diagram illustrating the relationship between these components.

2. Why is the study of binary logic important to the understanding of how computers work?

3. Using truth tables or otherwise, verify each of the following identities:
   1. 1.A = A
   2. A + (B+C) = (A+B) + C
   3. DeMorgan's Laws
   4. A + B.C = (A+B).(A+C)

4. Show how each of the following can be expressed using the NAND operator, and hence draw appropriate equivalents for the corresponding logic gate diagrams.
   1. not(A)
   2. A+B
   3. A.B
   4. A^B (exclusive OR)

5. Show that the expression
   not(A).not(B) + A.B + not(A).B can be simplified to B + not(A).

   Represent both expressions with appropriate logic gates. Finally express the simpler circuit entirely using NAND gates.

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