Binary: informing constituents

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Though binary counting and communication systems developed in many cultures around the world, modern information technology traces its roots back to ancient China. The German philosopher, mathematician, and logician Gottfried Wilhelm Leibniz (not the first European to discuss binary logic, just the most famous) learned binary counting from Jesuit missionaries, who in turn brought is from the Chinese—who also developed the decimal system, the place-value concept, the idea of zero and the symbol we use for it, the solution to indeterminate, quadratic and higher-order equations, modular arithmetic and the remainder theorem millennia before European scholars picked them up¹.

Boolean logic provides the second critical ingredient to information technology's use of the binary number system. Developed by George Boole in the mid-19th century, this abstract system of symbolic logic introduces the 'operators' AND, NOT, and OR, in addition to a few others. Boolean logic and binary mathematics were applied to electronic circuits by Claude Shannon at Massachusetts Institute of Technology in 1937, revolutionizing the design and operation of calculating machines, and paving the way for the computers we have today.

Computer software takes the data we enter, whether it's text, numbers, colored pixels, sounds, and other forms of input, and converts it to binary form for its calculations. As it completes calculations, it translates its results back into language we understand.

A binary number can be translated to a decimal number (34, 5, 893, etc.) through several methods, all involving powers of the base numeral 2. In one method, if you want to learn the decimal value of the binary number 101101, you take each digit (each 'bit': 1 or 0) and multiply it by the power of 2 it represents:

(1 x 2⁵) + (0 x 2⁴) + (1 x 2³) + (1 x 2²) + (0 x 2¹) + (1 x 2⁰)

or,

(1 x 32) + (0 x 16) + (1 x 8) + (1 x 4) + (0 x 2) + (1 x 1)

and simplified, it means

32 + 8 + 4 + 1 = 45

Conversely, to quickly learn the binary value of a given decimal number (such as 27), you divide it (and its dividends) by 2, and track the remainders:

27 / 2 = 13 remainder 1
13 / 2 = 6 remainder 1
6 / 2 = 3 remainder 0
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1

So, the binary value of 27 is 11011.

A combination of eight bits is called a 'byte'; the American Standard Code for Information Interchange (ASCII) uses bytes to translate letters to bytes and back again. For example, the letter "A" represents the byte 01000001. In today's computer terms, a 'kilobyte' represents 1,024 bytes (2¹⁰); a 'megabyte' represents 1,048,576 bytes (2²⁰); and a gigabyte equals 1,073,741,824 bytes (2³⁰).

In an age of information overload, there is more to know than ever before. How do you ensure that people understand what you have to offer—that they "get it"? How do you impart information, value, and benefits? How do inform and engage your constituents? Effective communications can make a difference.

Throughout our nearly quarter century of helping organizations achieve their goals, we have developed communication programs that inform a wide range of constituents for organizations of diverse scale and scope—start-up to centenarians. Explore our client credentials, learn more about how we think, follow the trail below to more information about binary counting, or contact us to learn how we can help you build effective communications systems.

1. McLeish 70.

For more information

McLeish, John. The story of numbers: how mathematics has shaped civilization. New York: Fawcett Columbine, 1994.

Binary Notation American Heritage Dictionary. 4th ed. 1999.

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