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Introduction toComputer Science
David Goldschmidt, Ph.D.Computer Science
The College of Saint Rose
CIS 111 06September 6, 2007
Binary Logic
At its lowest level, a computer operates on electrical current Voltage levels indicate ON or OFF An ON state represents binary digit 1 An OFF state represents binary digit 0
We use binary logic to describe binary variables and how they are processed Such processing is done by logical
circuits called gates
LogicGates
http://www.inetdaemon.com/tutorials/theory/number_systems/binary/gates.shtml
A logic gate is a logic device that accepts one or more binary inputs and produces one binary output
We combine these logic gates to build integrated circuits
Integrated Circuits (i)
Consider the following integrated circuit (IC):
What is x when A = 0, B = 1, and C = 1? What is x when A = 1, B = 1, and C = 1? What is x when A = 0, B = 0, and C = 0?
Integrated Circuits (ii)
Given the inputs to the following IC, what is x?
Boolean Logic Expressions (i)
http://www.inetdaemon.com/tutorials/theory/number_systems/binary/gates.shtml
We can write boolean logic expressions using the algebraic function notation from the chart
Boolean Logic Expressions (ii)
Consider the following IC:
The boolean logic expression is:
Write the truth table
_x = AB + C
Boolean Logic Expressions (iii)
Consider the following IC:
The boolean logic expression is:
Write the truth table
_ _x = AB(C + D)
Boolean Logic Expressions (iv)
Consider the following IC:
The boolean logic expression is:
Write the truth table
_x = A(A + B)
Boolean Logic Expressions (v)
Draw integrated circuits for the following boolean logic expressions:
_ _x = ABC _x = AB(C + D) _x = (A + B)(C + D) x = ABC
Write truth tables
for these ICs
Using the “Logg-O” Applet
Access Logg-O from the Analytical Engine CD or click on the image to go to the Web:
Get into teams of two or three
Do Lab 7.1 and Lab 7.2
Use “print-screen” to copy your answers into a Word document