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Table 3-1 The first 24 prime numbers The number 1 is not considered prime Any natural number, no matter how large, can be factored into a product of primes

Decimal The decimal number system is also called base 10 or radix 10 The set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} The first digit to the left of the radix or decimal point is multiplied by 100, or 1 The next digit to the left is multiplied by 101, or 10 The power of 10 increases as you move farther to the left The first digit to the right of the decimal point is multiplied by a factor of 10 1, or 1 10 The next digit to the right is multiplied by 10 2, or 1 100 This continues as you go farther to the right Once the process of multiplying each digit is completed, the resulting values are added up For example:

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Order 1st 2nd 3rd 4th 5th 6th 7th 8th Prime 2 3 5 7 11 13 17 19 Order 9th 10th 11th 12th 13th 14th 15th 16th Prime 23 29 31 37 41 43 47 53 Order 17th 18th 19th 20th 21st 22nd 23rd 24th Prime 59 61 67 71 73 79 83 89

The most direct way to get FM is to apply the audio signal to a varactor diode in a VFO circuit An example of this scheme, known as reactance modulation, is shown in Fig 26-10 The varying voltage across the varactor causes its capacitance to change in accordance with the audio waveform The changing capacitance results in an up-and-down swing in the frequency generated by the VFO In the illustration, only the tuned circuit of a Hartley oscillator is shown

the quotient are both factors of the original number Sometimes the quotient will be prime, and sometimes it won t be If it isn t prime, then it can be factored down further Don t stop dividing the original by primes until you get all the way down to 2 Once you ve found all the primes smaller than s that divide your original number without giving you a remainder, you have found the prime factors of your original number Some product of these will give you that original number You might find that one of the primes is a factor twice, three times, or more For example: 99 = 11 3 3 297 = 11 3 3 3 891 = 11 3 3 3 3 2,673 = 11 3 3 3 3 3

2 103 + 7 102 + 0 101 + 4 100 + 5 10 1 + 3 10 2 + 8 10 3 + 1 10 4 + 6 10 5 = 270453816

Perfect squares Whenever you multiply a number by itself, the process is called squaring, and the product is called a square If you multiply a natural number by itself, you get a perfect square If you take the square root of a perfect square, you always get a natural number Perfect squares, unlike primes, are easy to find if you have a calculator Table 3-2 lists the first 24 perfect squares, with 0 and 1 included

Another way to get FM is to modulate the phase of the oscillator signal This causes small fluctuations in the frequency as well, because any instantaneous phase change shows up as an instantaneous frequency change (and vice versa) This scheme is called phase modulation The circuit is more complicated than the reactance modulator When phase modulation is used, the audio signal must be processed, adjusting the amplitude versus-frequency response of the audio amplifiers Otherwise the signal will sound muffled in an FM receiver

Dividing through by 4, we get y = 2x + 4 Now for the second equation We begin with 7x y = 41 Subtracting 7x from each side, we get y = 7x + 41 Multiplying through by 1 gives us y = 7x 41

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