Digital electronics is a large branch of the electrical-electronics field relating to those electronic functions used in performing logical functions. It encompasses every type of logical system from simple combinational logic control in a coffee pot to the largest computer systems. The concept of digital control is not new. Even before the first computer appeared, or solid-state electronics came into being, large banks of relays were performing logical control functions in industrial facilities.
The earliest types of computers were called analog computers. They were enormous machines made from thousands of vacuum tubes. Computations were performed using voltage levels based on the decimal (base 10) numbering system. Although this method seems natural because you think in terms of tens (because you were created with 10 fingers), the old analog computers soon gave way to the more modern binary computers (base 2). There are very good reasons for this change, which will be explained as this chapter continues.
Although many people seem to have trouble comprehending different numbering systems, it’s really quite simple. The key is in understanding the mechanics behind the decimal system, and then applying those principles to any other numbering system.
The term decimal means “base 10.” If the number 1543 is broken down into decimal column weights, it comes out to 3 units (or ones), 4 tens, 5 hundreds, and 1 thousand. Notice how each succeeding weight is actually the base number (10) times the “weight” of the preceding column. In other words, 1 x 10 = 10, 10 x 10 = 100, 10 x 100 = 1000, and so on.
The binary numbering system works exactly the same way, except that it is based on 2 instead of 10. For example, the first weight (or least significant digit) is the units, or ones, column. The weight of the second column is 2 x 1, or 2. The next column is 2 x 2, or 4. The next column is 2 x 4, or 8. Instead of the column weights being ones, tens, hundreds, thousands, ten thousands, and so forth, the binary column weights will be ones, twos, fours, eights, sixteens, and so on.
In the decimal system, there are 10 possible numbers which can be placed in any weight column (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). In the binary system, there are only two possible numbers for any one weight column (a 0 or a 1; a “yes” or a “no”; an ON or an OFF). If a binary number such as 0111 is broken down into weights, it means 1 one, 1 two, 1 four, and 0 eights. By adding the weights together, the binary number can be converted to decimal. In the previous example, 1 + 2 + 4 = 7. Therefore, 0111 is the binary equivalent to decimal 7.
The following example demonstrates how it is possible to count up to 9 using the binary numbering system:
The binary numbering system is used in digital electronics because the binary digits 1 and 0 can be represented by an electronic device being either ON or OFF. For example, a relay can be energized or deenergized; or a transistor can be saturated or cut off. The advantage to a simple ON/OFF status is that the “absolute value or voltage level is not important.” In other words, it is totally irrelevant whether a transistor in cutoff has 4.5 volts, or 5.5 volts, on its collector. The only important data from a binary point of view is that it is OFF.
There are other numbering systems used extensively in digital electronics besides the binary system. The two most common ones are the octal system (base 8) and the hexadecimal system (base 16 system). These different numbering systems come in handy when interfacing with humans, but at the actual component level, everything is performed in binary.