3. Binary Circuit Encoding

Digital Computers and Binary Circuits

There are two basic types of computers:
digital computers, and
analog computers.

Analog computers tend to be used for special purpose applications which involve controlling manufacturing or similar "real-time" processes. They measure values using a continuous range (typically, a continuous range of electrical voltages) to manipulate environmental characteristics such as temperature and gas pressure. There has been a tendency over the past 10 or 20 years to replace this type of computer with digital computers which are connected to the "real-world" with "analog-to-digital" interface devices.

Digital computers are, by far, the more common type. They are the only type which we will consider in this course.

The main idea behind a digital computer is that, at least at a low level, values are represented using "descrete", rather than "continuous" units. Instead of a value being represented by any possible voltage between 0 volts and 5 volts (for example), a digital computer might require that the value be represented by one of the voltages: 0 volts, 1.5 volts, 3.0 volts, or 4.5 volts.

Some early digital computer systems used a 10-level representation scheme (which made working with our "normal" base 10 number system easy). Various other numbers of levels have been attempted with varying degrees of success. Modern digital computers, however, are restricted to a simple 2-level, or "binary" system.

As currently implemented, a "digital computer" is synonymous with a "computer which uses a binary system for value representation".

What is a "code"?

A "code" is a symbol which represents something else, a "real" or "abstract" entity.

(examples of codes)

(reasons for using codes). ..communication ..internal representation ..encryption (anti-open communication)

(one-to-one)(one-to-many)(many-to-one)

concept of domain; a piece of information identifies a particular possible entity within a domain; example, domain:season, entities: spring, summer, fall, winter; 4 codes are required; codes are not required for entities which are not part of the domain (no code is needed for "tree" or for 47).

Coding Schemes: Encoding and Decoding

encoding scheme method for determining the code to be used to represent some specific entity. single entity may only be "encoded" into one code value.

decoding scheme

coding system: combination of encoding and decoding schemes; one-to-one

entities may belong to many coding systems (same entity, different codes). codes may belong to many coding systems (same code, different entity)

tabular representation

encoding systems with no corresponding decoding systems

Binary Codes

a single binary code is extremely restrictive

codes composed of multiple binary values

Encoded Information versus Encoded Data

(the difference... review)

a code identifies a particular entity within a domain. in this sense a code provides "information" and not just "data" however....

in practice, we will use the terms interchangeably.