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Topic 4 Computer Mathematics and Logic

Introduction

Computer science is not a mathematics course. However, the following topics allow students to understand the basic principles of computer architecture, to understand the fundamental causes of many common errors, to design simple circuits, and to construct some common algorithms requiring mathematical techniques.

A.S.

Obj

4.2

Boolean Logic (5h)

4.2.1 1 Define the Boolean operators: and, or, not, nand, nor and xor, by drawing the appropriate truth table.
4.2.2 4 Construct Boolean expressions using the operators in 4.2.1.
     
Operator Symbol
and
or +
not (overbar)
xor

For example,

This can be written in words as: (A xor not B) and (C nor D)

4.2.3 3 Calculate the values of a Boolean expression using truth tables.
      A maximum of three inputs will be expected. Include the use of truth tables to determine whether two Boolean expressions are logically equivalent.
4.2.4 2 Convert Boolean expressions into simpler forms.
      A maximum of three inputs will be expected. Conversions may be done 'algebraically' (i.e. using identities such as x+1=1 and De Morgan's laws) or by using Karnaugh maps. Either method will be accepted in examinations.
4.2.5 4 Construct a logic circuit that corresponds to a specific Boolean expression by using standard logic gates.
      Symbols to be used for logic gates are given in Appendix 4. Circuits up to half-adder and full-adder must be constructed.
4.2.6 4 Construct a Boolean expression that corresponds to a specific logic circuit.
4.2.7 3 Explain the function of specific circuits.
 

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©Jeff Callard, February 2001
Last Updated:March 05, 2001