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Digital pertains to data in the form of digits. A digit is the unique numeric value used as a placeholder in some numbering system. As an example, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are all digits used in our base 10 numbering system. In communication systems, digital refers to the use of "digital" devices that use a binary numbering method to represent data. Confused? Binary refers to the possibility of having only one of two possible values, or states. In this instance, the value is either a zero or a one. So the terms digital signals, digital computers, digital transmission, etc., always refer to using binary signals (zeroes or ones) to represent the data, or information, that is being processed. "Digital" and "binary" are sometimes used interchangeably.
Figure 2-5. Representation of binary quantities
Binary signals are signals that assume one of two possible states, with each state characterized by its amplitude. See Figure 2-4. A one (1) is a high level, typically 2.5 to 5 volts, and a zero (0) is 0 to 1.5 volts. Of course, different families of logic types, such as Transistor-Transistor Logic (TTL) and Complementary Metal Oxide Semiconductor (CMOS), have different levels for ones values with 0 volts the usual zero value. But for learning purposes, assume a logic one of 5 volts and a logic zero of 0 volts, as appropriate.
A single binary value is called a bit, also known as a pulse. A bit may be either a one or a zero. Figure 2-5 shows a bit as a binary value of one. A single bit by itself is only useful for representing one of two possible states (one or zero). To represent addi0tional states, additional bits must be included in some manner. For the math hounds, you can represent (x^n) states (things) with x^n digits. That is, four digits (or bits, same thing) can represent 16 values. That is, the decimal numbers 0-15 can be represented with four digits.
Typically, bits are grouped as follows: four bits make a nibble, eight bits make a byte (pronounced bite), 16 bits make a word, and 32 bits make a double word. When two or more words are grouped together, a data stream is formed. Sometimes, a byte is called an octet.
The rate at which binary signals are passed along from device to device is called the period (measured in seconds). Usually, the period is measured from the leading edge to the trailing edge of the pulse. The frequency of the bit stream is the number of periods in any given second.
Figure 2-6. Converting an analog signal
2-Input AND Gate | 2-Input NAND Gate | ||||
Possible Inputs | Possible Outputs | Possible Inputs | Possible Outputs | ||
Input A | Input B | Output C | Input A | Input B | Output C |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 0 |
Table 2-1. Digital AND and NAND gates (digital "state machines")
The use of digital integrated circuits and the continued reduction in circuit geometry is responsible for the breathtaking evolution in technology in the last 20 years. A common digital circuit is the AND device, also called an AND gate. The AND gate "ands" the inputs to give a particular output in accordance with the specific combination of inputs. An AND gate may have more than two inputs but will always have one output. From Table 2-1 you may see that the output is always zero (low) until all the inputs are high, and then the output switches to a one (high). The NAND function is just the opposite of the AND function.
Figure 2-7. Simplified pulse amplitude modulation
2-Input OR Gate | 2-Input NOR Gate | ||||
Possible Inputs | Possible Outputs | Possible Inputs | Possible Outputs | ||
Input A | Input B | Output C | Input A | Input B | Output C |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 |
Figure 2-8 Single polarity PAM
Table 2-2. Digital OR and NOR gates
The OR gate output is always high if any input is high. See Table 2-2. The NOR function is just the opposite of the OR function. There are many types of digital devices, but almost all of them are composed of a few fundamental gate types such as the AND and OR and their logical inverses, the NAND and NOR gates. Using the AND and OR gates, one can construct a wonderful array of very useful digital devices.
An analog signal can be represented by a series of digital pulses. The particular circuit that performs an analog-to-digital signal conversion is called, appropriately enough, an analog-to-digital converter, or ADC. An ADC circuit samples the analog signal to be converted at periodic intervals and generates a binary value representing the value of the sampled voltage. See Figure 2-6. Periodically, at the points in time designated by A, B, C, etc., the analog signal level is measured. The measured signal level is converted to a digital number representing that level. See the table in Figure 2-6. As an example, the voltage measured in time indicated by point E is 4 volts. Our ADC converter will output the digital bits corresponding to 0100 to represent the 4-volt level at point E.
Converting a digital signal back to an analog signal is the reverse of the analog-to-digital signal conversion process. The circuit that performs the digital-to-analog signal conversion is called, appropriately enough, a digital-to-analog converter, or DAC. The DAC outputs a voltage corresponding to the value of the set of bits received. In our previous example, the ADC converted 4 volts to the digital bit stream 0100. Now, the DAC will convert the digital bit stream 0100 to 4 volts.
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