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Q&A #2926 |
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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