Binary Number

Pronunciation: /ˈbaɪ nɛ ri ˈnʌm bər/ Explain

A binary number is a number expressed in a base 2 counting system.[1] In a base 2 counting system, there are only 2 digits: 0 and 1.

9 = 1001 base 2, 9 = 1x8 + 0x4 + 0x2 + 1x1
Figure 1: 910 = 10012

Figure 1 illustrates that 9 in decimal (base 10) is equal to 1001 in binary (base 2). In decimal, the first four place values to the left of the decimal are:

1 = 100,
10 = 101,
100 = 102, and
1000 = 103.
In decimal (base 10), each place value is 10 times the previous place value.

In binary the first four places values are:

1 = 20,
2 = 21,
4 = 22, and
8 = 23.
In binary (base 2) each place value is 2 times the previous place value. So 10012 = 1·8 + 0·4 + 0·2 + 1·1 = 9.

Saying numbers in binary

When reading numbers in binary, don't use the terms 'hundred' and 'thousand'. These words are defined only for the decimal numeration. 10012 is said, "One oh oh one base two". When speaking, the word 'oh' is short for zero.

References

  1. binary. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/19/2018. http://www.merriam-webster.com/dictionary/binary number.
  2. Conant, Levi Leonard, Ph.D.. The Number Concept, Its Origin and Development. pg 102. www.archive.org. Macmillan and Company. 1896. Last Accessed 6/19/2018. http://www.archive.org/stream/cu31924059316087#page/n117/mode/1up/search/binary. Buy the book

More Information

  • McAdams, David E.. Binary. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/22/2018. http://www.allmathwords.org/en/b/binary.html.

Cite this article as:

McAdams, David E. Binary Number. 6/19/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/binarynumber.html.

Image Credits

Revision History

6/22/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/8/2010: Added "References". (McAdams, David E.)
6/24/2008: Changed color scheme. (McAdams, David E.)
4/18/2008: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License