2 Chapter 1 Digital Systems and Binary Numbers
called signals. Electrical signals such as voltages and currents are the most common.
Electronic devices called transistors predominate in the circuitry that implements these
signals. The signals in most presentday electronic digital systems use just two discrete
values and are therefore said to be binary. A binary digit, called a bit, has two values: 0
and 1. Discrete elements of information are represented with groups of bits called binary
codes. For example, the decimal digits 0 through 9 are represented in a digital system
with a code of four bits (e.g., the number 7 is represented by 0111). How a pattern of
bits is interpreted as a number depends on the code system in which it resides. To make
this distinction, we could write (0111)
2
to indicate that the pattern 0111 is to be inter-
preted in a binary system, and (0111)
10
to indicate that the reference system is decimal.
Then 0111
2
= 7
10
, which is not the same as 0111
10
, or one hundred eleven. The subscript
indicating the base for interpreting a pattern of bits will be used only when clarification
is needed. Through various techniques, groups of bits can be made to represent discrete
symbols, not necessarily numbers, which are then used to develop the system in a digital
format. Thus, a digital system is a system that manipulates discrete elements of informa-
tion represented internally in binary form. In today’s technology, binary systems are most
practical because, as we will see, they can be implemented with electronic components.
Discrete quantities of information either emerge from the nature of the data being
processed or may be quantized from a continuous process. On the one hand, a payroll
schedule is an inherently discrete process that contains employee names, social security
numbers, weekly salaries, income taxes, and so on. An employee’s paycheck is processed
by means of discrete data values such as letters of the alphabet (names), digits (salary),
and special symbols (such as $). On the other hand, a research scientist may observe a
continuous process, but record only specific quantities in tabular form. The scientist is
thus quantizing continuous data, making each number in his or her table a discrete
quantity. In many cases, the quantization of a process can be performed automatically
by an analogtodigital converter, a device that forms a digital (discrete) representation
of a analog (continuous) quantity.
The generalpurpose digital computer is the bestknown example of a digital system.
The major parts of a computer are a memory unit, a central processing unit, and input–
output units. The memory unit stores programs as well as input, output, and intermedi-
ate data. The central processing unit performs arithmetic and other dataprocessing
operations as specified by the program. The program and data prepared by a user are
transferred into memory by means of an input device such as a keyboard. An output
device, such as a printer, receives the results of the computations, and the printed results
are presented to the user. A digital computer can accommodate many input and output
devices. One very useful device is a communication unit that provides interaction with
other users through the Internet. A digital computer is a powerful instrument that can
perform not only arithmetic computations, but also logical operations. In addition, it can
be programmed to make decisions based on internal and external conditions.
There are fundamental reasons that commercial products are made with digital cir-
cuits. Like a digital computer, most digital devices are programmable. By changing the
program in a programmable device, the same underlying hardware can be used for many
different applications, thereby allowing its cost of development to be spread across a
wider customer base. Dramatic cost reductions in digital devices have come about