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:
9_{10} = 1001_{2} 
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 = 10^{0}, 
10 = 10^{1}, 
100 = 10^{2}, and 
1000 = 10^{3}. 
In decimal (base
10), each place value is
10 times the previous place value.
In binary the first four places values are:
1 = 2^{0}, 
2 = 2^{1}, 
4 = 2^{2}, and 
8 = 2^{3}. 
In binary (base
2) each place value is
2 times the previous place value. So
1001_{2} = 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.
1001_{2} is said, "One oh oh one base two".
When speaking, the word 'oh' is short for zero.
References
 McAdams, David E.. All Math Words Dictionary, binary number. 2nd Classroom edition 201501084799968. pg 26. Life is a Story Problem LLC. January 8, 2015. Buy the book
 binary. merriamwebster.com. Encyclopedia Britannica. MerriamWebster. Last Accessed 6/19/2018. http://www.merriamwebster.com/dictionary/binary number. Buy the book
 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
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.)