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There are two distinct families of computing devices, namely, digital computers
and the historical analog computer. These two types of computer operate on quite
different principles, and the earliest computers were analog not digital.
The representation of data in an analog computer reects the properties of the
data that is being modeled. For example, data and numbers may be represented by
physical quantities such as electric voltage in an analog computer, whereas in a digi-
tal computer, a stream of binary digits is used.
A digital computer is a sequential device that generally operates on the data one
step at a time. The data in a digital computer are represented in binary format, which
employs just two digits, namely, 0 and 1. A single transistor has two states, i.e., on
and off, and is used to represent a single binary digit. Several transistors are used to
represent larger numbers.
Early computing devices include the slide rule and various mechanical calcula-
tors. William Oughtred and others invented the slide rule in 1622, and it allowed
multiplication and division to be carried out signicantly faster than calculation by
hand. Blaise Pascal invented the rst mechanical calculator in 1642. It was called
the Pascaline, and it could add or subtract two numbers. Multiplication or division
could not be performed directly but could instead be carried out by repeated addi-
tion or subtraction.
Leibniz
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invented a mechanical calculator (called the Step Reckoner) in 1672.
This was the rst calculator that could perform all four arithmetic operations: i.e.,
addition, subtraction, multiplication, and division.
James Thompson (who was the brother of Lord Kelvin) did early work on analog
computation in the nineteenth century. He invented a wheel and disk integrator,
which was used in mechanical analog devices, and he worked with Kelvin to con-
struct a device to perform the integration of a product of two functions.
The operations in an analog computer are performed in parallel, and they are
useful in simulating dynamic systems. They have been applied to ight simulation,
nuclear power plants, and industrial chemical processes.
Vannevar Bush and others developed the rst large-scale general-purpose
mechanical analog computer at Massachusetts Institute of Technology in the late
1920s (Fig.1.1). Bush’s differential analyzer was designed to solve sixth order dif-
ferential equations by integration, using wheel-and-disk mechanisms to perform the
integration. The machine enabled integration and differential equation problems to
be solved more rapidly.
The machine consisted of wheels, disks, shafts, and gears to perform the calcula-
tions, and it required signicant effort to be set up by technicians to solve a particu-
lar problem. It contained 150 motors and miles of wires connecting relays and
vacuum tubes.
Data representation in an analog computer is compact, but it may be subject to
corruption with noise. A single capacitor can store one continuous variable in an
analog computer, whereas several transistors are required to represent a variable in
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Leibniz is credited (along with Newton) with the development of the Calculus.
1 Background