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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 have trouble 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 the attainable states are as few as possible: two. High or low. Logic 1 or 0. On/off. Yes/no.
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On a single wire or line, a binary digital signal is either full-on or full-off at any given moment. These are the logic high and low, and are represented by dc voltages. The high voltage is approximately 3 V to 5 V, and the low voltage is between 0 V and 2 V.
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A binary number has several binary digits, or bits. The number of bits depends on how big the 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 want to be able to transmit numbers as high as 11111111, or the decimal 0 to 255, you need eight 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 number of lines corresponds to the number of bits in the binary number. That is, in order to send binary numbers up to 1111, you need four lines; to send numbers up to 11111111, you
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558 Basic digital principles need eight lines. This is called parallel data transfer, because the bits are sent along lines that are effectively in parallel with each other (Fig. 30-1). Clearly, parallel data transfer has limitations. For large numbers, it would need many lines. This can present certain logistic problems, for example in long-distance radio or wire transmission.
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30-1 Parallel data transfer of the binary number 0110.
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In radio communications using parallel data transfer, each line must correspond to a different frequency; the result is that large binary numbers need many channels. This translates into a wide signal bandwidth. The necessary bandwidth is not always easy to obtain. It is especially difficult at low and shortwave frequencies, where wideband signals present not only an engineering hassle, but tend to hog spectrum space. Fortunately, there is another way to send binary data, and this method needs only one line or radio frequency. It is called serial data transfer. Instead of sending each bit on a separate line, the bits are transmitted one after the other in a defined sequence. To send binary numbers up to 1111 serially, you need four time slots. For the serial transmission of binary numbers up to 11111111, you need eight slots. Each slot has a certain duration. Generally, all the slots are of equal length. A four-bit serial signal is shown in Fig. 30-2.
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30-2 Serial representation of the binary number 0110.
Suppose the duration of a bit is 1 ms (a millisecond). The bit rate is then 1,000 bits per second (bps). In general, if the bit duration in seconds is t, then the bps rate is 1/t. Radio data-communications systems operate at speeds upwards of 10,000 bps, or 10 kbps. Serial data transfer is somewhat slower than parallel transfer. This is the necessary tradeoff for the convenience of a single transmission line, or for narrower radio-signal bandwidth. In electronics, as in life, you never get something for nothing.
Basic logic operations 559
Positive versus negative logic
Usually, logic 1 is high and logic 0 is low. This is known as positive logic. But these states can be reversed, and the results will be just as good. When logic 1 is low and logic 0 is high (so that a bit 1 is off and a bit 0 is on ), negative logic is being used. In the rest of this chapter, positive logic is the rule. This is simply to minimize confusion.
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