Digital and Binary, Binary and Digital

Clarifying the relativity between the two words

Elevation, subtitled “A view of the U.K. Lift Industry,” is a magazine published by Ish Buckingham. In one of its past issues, David Cooper posed an inquiry to the readership seeking clarification on the relationship between digital and binary. Cooper wrote:

“I found myself in a debate recently about the relativity between the words binary and digital. . . . Three stances were finally agreed on by different people who could not come to a consensus. I wonder if you could ask your readers.”

The three stances agreed upon as possible are:

• Binary is digital; digital is binary.
• Binary is digital; digital includes binary.
• Binary is digital; digital means binary.

In response, there followed a brief tutorial by Dr. Gina Barney in a subsequent Elevation issue on various numbering systems, including the hexidecimal and decimal systems. My interest in the topic prompted me to submit a response to Elevation and Cooper’s inquiry, which follows.

Digital electronics is a method of transmitting signals where discrete values of electromagnetic or photoelectric energy are transmitted from one place to another. At frequencies lower than those in the electromagnetic spectrum are sounds (the compression and rarefaction of air) that can be digitized to transmit an audible signal.

While digital signals can take on several values, two states are typically used – “On” or “Off,” “Yes” or “No,” “1” or “0.” The digital signals are generated by “slicing” analog signals into discrete bands of voltage, frequency or other characteristics of electromagnetic or photoelectric energy. Each value or state will be represented by a band of frequencies or a range of voltages. Thus, a “0” or “No” could be represented by something near 0 V, and a “1” or “Yes” by something near 5 V. There is no hard and fast rule as to how many discrete bands into which the signal should be divided. It could be three bands or states, or even four or five. In the case where three distinct states are used, a tertiary numbering system might be appropriate.

Some early uses of digital signal transmission are Morse code or signal lamps. One could even say the smoke signals used by Native Americans were a form of digital signal. So far I’ve been careful to not use the term “communication.” The purpose of the signal, be it via electromagnetic, light, sound or smoke, is to transmit information and thus communicate. In order to transmit information, some code or language needs to be applied to the digital signals.

Samuel Morse opted to use dots and dashes (short and long sounds) in various combinations to represent the various letters of the alphabet and numbers. The same Morse code was ultimately applied to signal lamps used by navies to transmit information and lights to and from other ships.

So, while digital signal transmission has been around for a long time in one form or another, its utility comes from the ability to transmit information. Where information is transmitted via digital electromagnetic energy, it has proven expedient to utilize two states or values as described above. The code or language used to turn the signal into information is the binary code (binary numbering system).

The binary numbering system and binary logic were developed by George Boole, allowing sophisticated, complex information to be transmitted by using digital signals such as “1” and “0.” This information can be manipulated to perform mathematical functions. In today’s world of computers and digital electronics, the binary digits or “bits” are transmitted and lumped into groups of eight binary digits (“1” and “0”) called “bytes.” These bytes can represent up to 256 different characters (0-255). Zero = 0000 0000, and 255 = 1111 1111. The value of the byte is determined by the intended use of the information. It might represent the various letters of the alphabet and symbols as in the American Standard Code for Information Interchange code set, or it could simply represent a group of numbers.

The use of Boolean algebra, which is the algebra of truth values, enables all the mathematical functions (multiplication, division, addition and subtraction) to be performed. The binary system has been used in computers since the days of Charles Babbage and Alan Turing. The use of the binary code in modern computers enables us to manipulate these bits and bytes at tremendous speeds.

Given the three choices offered in the initial question, the better answer is, “Binary is digital; digital includes binary.” This is, perhaps, an oversimplification. I would prefer to say, “The binary numbering system or binary logic is a language used to transmit information via digital signals. This same type of relationship was expressed at one time by Richard Feynman when he explained the relationship between physics and other sciences when he implied mathematics was the language of physics. That is to say, the physical laws are expressed as mathematical formulae.”

When trying to explain relationships to the masses, one should use caution so as not to oversimplify the terms to a point where they may be misunderstood by everyone. I trust the foregoing addresses the question posed in Cooper’s article.

Reprinted from Elevation.

© 2011, Davis L. Turner