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Q&A #2926


Boolean Algebra

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From: Claudia (for Teacher2Teacher Service)
Date: Feb 15, 2000 at 23:25:47
Subject: Re: Boolean Algebra

Ok -- so here's one way addition works -- not the favored algorithm,
but the easiest to demonstrate.

Full Adder with Carry

At the hardware level, every FA cell has 3 inputs
the two bits to be added and the carry in;
Each cell also has two outputs, the sum of the inputs and the
carry out.

A full adder cell behaves as follows

output 0 carry out 0 + 0 = output 0 carry out 0
output 0 carry out 0 + 1 =  output 1 carry out 0

output 1 carry out 0 + 0 = output 1 carry out 0
output 1 carry out 0 + 1 = output 0 carry out 1

output 0 carry out 1 + 0 = output 0 carry out 1
output 0 carry out 1 + 1 = output 1 carry out 1

or

output = input1 xor input2 xor carry in
carry out = (input1 and input2) or (carry in and (input 1 or input2))

To model this with students --

Every student represents a full adder cell --
each cell starts with an initial output of 0 and a carry out of 0
the first cell has an implied carry in of 0.

We adopt the following notation --
input:
 a tap is a 1
 a point is a 0
output:
 a left arm across the chest is a 1
 a left arm at the side is a 0
 a right arm at the side is a 0 carry-out
 a right arm outstretched to tap his neighbor is a 1 carry-out.

The student cells behave as follows:
no change of state occurs on a point
first tap -- left arm across chest, right arm at side
second tap -- left arm at side, right arm outstretched
third tap -- left arm across chest, right arm outstretched.

-- hope this helps

 -Claudia, for the Teacher2Teacher service

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