Binary Number

Pronunciation: /ˈbaɪ.nɛ.ri ˈnʌm.bər/ Explain

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

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. McAdams, David E.. All Math Words Dictionary, binary number. 2nd Classroom edition 20150108-4799968. pg 26. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. binary. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/19/2018. http://www.merriam-webster.com/dictionary/binary number. Buy the book
3. 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. https://www.allmathwords.org/en/b/binary.html.

Cite this article as:

McAdams, David E. Binary Number. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/b/binarynumber.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/12/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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.)