| A very simple computerPARTS AND MATERIALS  
                      
                      Three batteries, each one with a different 
                      voltage 
                      Three equal-value resistors, between 10 kΩ 
                      and 47 kΩ each  When selecting resistors, measure each one 
                    with an ohmmeter and choose three that are the closest in 
                    value to each other. Precision is very important for this 
                    experiment!    CROSS-REFERENCES  Lessons In Electric Circuits, Volume 
                    1, chapter 10: "DC Network Analysis"    LEARNING OBJECTIVES  SCHEMATIC DIAGRAM  
                      
 
 ILLUSTRATION  
                        
 
 
                      
 
 INSTRUCTIONS  This deceptively crude circuit performs the 
                    function of mathematically averaging three voltage 
                    signals together, and so fulfills a specialized 
                    computational role. In other words, it is a computer that 
                    can only do one mathematical operation: averaging three 
                    quantities together.  Build this circuit as shown and measure all 
                    battery voltages with a voltmeter. Write these voltage 
                    figures on paper and average them together (E1 + 
                    E2 + E3, divided by three). When you 
                    measure each battery voltage, keep the black test probe 
                    connected to the "ground" point (the side of the battery 
                    directly joined to the other batteries by jumper wires), and 
                    touch the red probe to the other battery terminal. Polarity 
                    is important here! You will notice one battery in the 
                    schematic diagram connected "backward" to the other two, 
                    negative side "up." This battery's voltage should read as a 
                    negative quantity when measured by a properly connected 
                    digital meter, the other batteries measuring positive.  When the voltmeter is connected to the 
                    circuit at the point shown in the schematic and 
                    illustrations, it should register the algebraic average of 
                    the three batteries' voltages. If the resistor values are 
                    chosen to match each other very closely, the "output" 
                    voltage of this circuit should match the calculated average 
                    very closely as well.  If one battery is disconnected, the output 
                    voltage will equal the average voltage of the remaining 
                    batteries. If the jumper wires formerly connecting the 
                    removed battery to the averager circuit are connected to 
                    each other, the circuit will average the two remaining 
                    voltages together with 0 volts, producing a smaller output 
                    signal:  
                      The sheer simplicity of this circuit deters 
                    most people from calling it a "computer," but it undeniably 
                    performs the mathematical function of averaging. Not only 
                    does it perform this function, but it performs it much 
                    faster than any modern digital computer can! Digital 
                    computers, such as personal computers (PCs) and pushbutton 
                    calculators, perform mathematical operations in a series of 
                    discrete steps. Analog computers perform calculations in 
                    continuous fashion, exploiting Ohm's and Kirchhoff's Laws 
                    for an arithmetic purpose, the "answer" computed as fast as 
                    voltage propagates through the circuit (ideally, at the 
                    speed of light!).  With the addition of circuits called 
                    amplifiers, voltage signals in analog computer networks 
                    may be boosted and re-used in other networks to perform a 
                    wide variety of mathematical functions. Such analog 
                    computers excel at performing the calculus operations of 
                    numerical differentiation and integration, and as such may 
                    be used to simulate the behavior of complex mechanical, 
                    electrical, and even chemical systems. At one time, analog 
                    computers were the ultimate tool for engineering research, 
                    but since then have been largely supplanted by digital 
                    computer technology. Digital computers enjoy the advantage 
                    of performing mathematical operations with much better 
                    precision than analog computers, albeit at much slower 
                    theoretical speeds.  
 
 COMPUTER SIMULATION  Schematic with SPICE node numbers:
                     
                      
 
 Netlist (make a text file containing the 
                    following text, verbatim):  Voltage averager
v1 1 0
v2 0 2 dc 9
v3 3 0 dc 1.5
r1 1 4 10k
r2 2 4 10k
r3 3 4 10k
.dc v1 6 6 1
.print dc v(4,0)
.end
 With this SPICE netlist, we can force a 
                    digital computer to simulate and analog computer, which 
                    averages three numbers together. Obviously, we aren't doing 
                    this for the practical task of averaging numbers, but rather 
                    to learn more about circuits and more about computer 
                    simulation of circuits! 
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