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of time the use of a dual voltage AC power supply is recommended The diagram shown in Figure 19-4 illustrates a simple dual plus and minus voltage power supply which can be used to power the SIDs receiver A 9 volt 500 mA center tapped transformer was used to drive a bridge rectifier, which provides both a plus and minus voltage that is sent to a 9 volt plus regulator An LM78L09 regulator and the minus leg of the bridge is sent to an LM79L09 minus 9 volt regulator The power supply could be built on perf-board or on a printed circuit board if desired The power supply and SIDs receiver could be mounted alongside one another in the same chassis Take a short break and when we return we will inspect the circuit board for any possible cold solder joints or short circuits Pick up the circuit board so that the foil side of the PC board faces upwards toward you Look over the foil side of the board very carefully The solder joints should all look clean, bright and shiny If you see any solder joints that look dull, dark, dirty or blobby then you should remove the solder and re-solder the joint so that it looks clean, bright and shiny Next we are going to inspect the PC board for any possible short circuits Sometimes cut component leads will stick to the board from solder residue left on the board These stray wires can often cause a short between the solder traces Also look closely for any solder blob or solder balls, which may have stuck to the underside of the PC board The SIDs receiver and power supply can both be installed in a metal chassis box enclosure The prototype receiver was mounted in a sloping cabinet as in Figure 19-1 The power supply was mounted alongside.

We started out with the natural numbers (or naturals), and took their negatives to get the integers Then we divided integers by each other to come up with rational numbers (or rationals) In this chapter, we ll study the irrational numbers (or irrationals) and real numbers (or reals), and compile a full set of rules for working with real variables

1 3 1 2 3

Mathematicians have known for centuries that there are plenty of irrational numbers that can t be expressed as ratios of integers Let s see how they behave compared with the rational numbers

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Rational-number density Suppose we assign rational numbers to points on a horizontal line so the distance of any point from the origin is directly proportional to its absolute value If a point is on the left-hand side of the point representing 0, then that point corresponds to a negative number; if it s on the right-hand side, it corresponds to a positive number If we take any two points a and b on the line that correspond to rational numbers, then the point midway between them corresponds to the rational number (a + b)/2 (Do you recognize this as the formula for the average, or arithmetic mean, of two numbers ) We can keep cutting an interval in half, and if the end points are both rational numbers, then the midpoint is another rational number Figure 9-1 shows an example of this, starting with the interval between 1 and 2 It is tempting to suppose that the points on a rational-number line are infinitely dense The point midway between any two rational-number points always corresponds to another rational number But do the rational numbers account for all of the points along a true geometric line The answer is No They don t even come close! Irrational numbers As we have seen, an irrational number can t be expressed as the ratio of two integers Examples of irrational numbers include:

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