### Binary Digital Communications

The use of binary data provides excellent communications accuracy and efficiency. If multilevel signaling is required, then all the levels can be represented by groups of binary digits. A group of 3 binary digits, for example, can represent 23, or 8, levels. A group of 4 binary digits can represent 24, or 16, levels. The term binary digit is commonly contracted to bit.

#### Bits, Bytes, and Baud

A bit is almost always represented by either 0 or 1. A group of 8 bits is a called an octet, and in many systems this also corresponds to a unit called a byte. Large quantities of data can be expressed either according to powers of 2, or according to powers of 10. This can cause some confusion and gives rise to endless debates over semantics.

One kilobit (kb) is equal to 1000 bits. A megabit (Mb) is 1000 kilobits, or 1,000,000 bits. A gigabit (Gb) is 1000 megabits, or 1,000,000,000 bits. When data is expressed in bits, powers of 10 are used to define large quantities. If you hear about a modem that operates at 56 kbps, it means 56,000 bits per second (bps). Bits, kilobits, megabits, and gigabits per second (bps, kbps, Mbps, and Gbps) are commonly used to express data in communications.

Data quantity in storage and memory is usually specified in kilobytes (units of 210 = 1,024 bytes), megabytes (units of 220 = 1,048,576 bytes), and gigabytes (units of 230 = 1,073,741,824 bytes). The abbreviations for these units are KB, MB, and GB, respectively. Note that the uppercase K represents 210 or 1024, while the lowercase k represents 103 or 1000. But M and G are always uppercase, no matter whether powers of 2 or 10 are used. (Is all of this confusing to you? Don’t be discouraged. It confuses almost everybody.)

Larger data units are being used as memory and storage media continue to grow. The terabyte (TB) is 240 bytes, or 1024 GB. The petabyte (PB) is 250 bytes, or 1024 TB. The exabyte (EB) is 260 bytes, or 1024 PB. The term baud refers to the number of times per second that a signal changes state. The units of bps and baud are not equivalent, even though people often speak of them as if they are. These
days, baud (or “baud rate”) is seldom used to express data speed. When computers are linked in a network, each computer has a modem (modulator/demodulator) connecting it to the communications medium. The slowest modem determines the speed at which the machines communicate. below Table shows common data speeds and the approximate time periods required to send 1, 10, and 100 pages of double-spaced, typewritten text at each speed.
A:

Speed, kbps Time for one page Time for 10 pages Time for 100 pages
28.8 0.38s 3.8 s 38 s
38.4 280 ms 2.8 s 28 s
57.6 190 ms 1.9 s 19 s
100 110 ms 1.1 ms 11 s
250 44 ms 440 ms 4.4 s
500 22 ms 220 ms 2.2 s

B:

Speed, Mbps Time for one page Time for 10 pages Time for 100 pages
1.00 11 ms 110 ms 1.1 s
2.50 4.4 ms 44 ms 440 ms
10.0 1.1 ms 11 ms 110 ms
100 110 μs 1.1 ms 11 ms

#### Forms of Conversion

An analog waveform (dashed curve) and an 8-level digital representation (vertical bars).
Any analog (continuously variable) signal can be converted into a string of pulses whose amplitudes have a finite number of states, usually some power of 2. This is analog-to-digital (A/D) conversion, and its reverse is digital-to-analog (D/A) conversion, as you’ve already learned. The difference between analog and digital signals can be intuitively seen by examining above figure. This is essentially a rendition of 8-level pulse code modulation (PCM).

Binary digital data can be sent and received one bit at a time along a single line or channel. This is serial data transmission. Higher data speeds can be obtained by using multiple lines or a wideband channel, sending independent sequences of bits along each line or subchannel. This is parallel data transmission.

Parallel-to-serial (P/S) conversion receives bits from multiple lines or channels, and transmits them one at a time along a single line or channel. A buffer stores the bits from the parallel lines or channels while they are awaiting transmission along the serial line or channel. Serial-to-parallel (S/P) conversion receives bits from a serial line or channel, and sends them in batches along several lines or channels. The output of an S/P converter cannot go any faster than the input, but the circuit is useful when it is necessary to interface between a serial-data device and a parallel-data device.

Below figure illustrates a circuit in which a P/S converter is used at the source (transmitting station), and an S/P converter is used at the destination (receiving station). In this example, the words are 8-bit bytes. However, the words could have 16, 32, 64, or even 128 bits, depending on the communications scheme.

A communications circuit employing parallel-to-serial (P/S) conversion at the source, and serial to parallel (S/P) conversion at the destination.

#### Data Compression

At A, a packet-wireless station. At B, passage of a packet through nodes in a wireless communications circuit.
Data compression is a way of maximizing the amount of digital information that can be stored in a given space, or sent in a certain period of time. Text files can be compressed by replacing often-used words and phrases with symbols such as =, #, &, \$, and @, as long as none of these symbols occurs in the uncompressed file. When the data is received, it is uncompressed by substituting the original words and phrases for the symbols.
Digital images can be compressed in either of two ways. In lossless image compression, detail is not sacrificed; only the redundant bits are eliminated. In lossy image compression, some detail is lost, although the loss is usually not significant.

#### Packet Wireless

In packet wireless, a computer is connected to a radio transceiver using a terminal node controller (TNC), which is similar to a modem. An example is shown in above figure A. The computer has a telephone modem as well as a TNC, so messages can be sent and received using conventional online