# Binary Number

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

A binary number is a number expressed in a base 2 counting system. 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.

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

• 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.

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.

### 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.)