Logic signals

Chapter Logic signals

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • In general, the nth place from the right has the decimal value 2n. The total decimalvalue, for a given binary number, is the sum of the decimal values of each of the places.Converting decimal numbers to binary form can be done using Table 30-1. Sup-pose, for example, that you want to convert 35912 to binary notation. First, find thelargest decimal number on the table that is no greater than the decimal number youwish to convert. In this case, it is 32768 215 .From this, you know that there will be 16digits in the binary representation of this number, one for each place 20 through 215.Mark off 16 slots or spaces on a sheet of paper (quadrille graph paper is perfect for this),and place a digit “1” in the left-most space, representing 215.Now, use Table 30-1 to determine which number can be added to 32768 to get thelargest decimal number that doesn’t exceed 35912. It happens to be 2048 211. Placedigits “0” in the slots for 214, 213, and 212. Then place “1” in the space for 211.If you continue this process, you’ll ultimately get the binary number1000110001001000. This 16-digit binary number is equivalent to the decimal 35912 864102420483276823 26210+ 211215. The slots for exponents 3, 6,10, 11, and 15 each are filled with binary digit 1; the others are filled with binary digit 0.It is possible to have fractional values in binary notation, just as it is in decimal no-tation. The first place to the right of the point (perhaps best called a “binary point”rather than a “decimal point”) is the 1/2’s place (2-1). The next place is the 1/4’s place(2-2); then comes the 1/8’s place (2-3), and so on. Thus, 0.001 in binary notation repre-sents the decimal fraction 1/8. You can think of it as repeatedly dividing the size in halfas you progress towards the right.Why use such cumbersome notation?Perhaps you’ve noticed that binary notation gets into long number strings. This is true.(Try writing the decimal quadrillion, or 1015, in binary form!) But computers don’t havetrouble dealing with long strings of digits. That’s what we build them for! To a computer,the important thing is to be certain of the value of each digit. This is easiest when theattainable states are as few as possible: two. High or low. Logic 1 or 0. On/off. Yes/no.Logic signalsOn a single wire or line, a binary digital signal is either full-on or full-off at any given mo-ment. These are the logic high and low, and are represented by dc voltages. The highvoltage is approximately 3 V to 5 V, and the low voltage is between 0 V and 2 V.Parallel data transferA binary number has several binary digits, or bits. The number of bits depends on how bigthe numbers can get. For example, if you want to send binary numbers from 0000 to 1111(which corresponds to the decimal numbers 0 through 15), you need four bits. If you wantto be able to transmit numbers as high as 11111111, or the decimal 0 to 255, you needeight bits. For large decimal numbers, you’ll need many bits—sometimes several dozen.The bits can be sent along separate wires or lines. When this is done, the numberof lines corresponds to the number of bits in the binary number. That is, in order to sendbinary numbers up to 1111, you need four lines; to send numbers up to 11111111, youLogic signals557