Data Representations – Binaries and Decimals

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In digital systems like computers, data is represented by symbols called digits. We are used to counting digits in 10s. However, computers count in 2s. What does that mean?


The base or radix of a number system is defined as the number of different digits which can occur in each position in the number system. For example, the decimal number system has a base, or radix, of 10, since the system has 10 different digits (0,1,2,…9), any one of which may be used in each position in a number.

Decimal Number System

The decimal system is composed of 10 numerals or symbols, 0,1,2,…9. (Deca means 10, that is why this system is called decimal system). Using these symbols as digits of a number, we can express any quantity. The decimal system is also called the base-10 system because it has 10 digits.

Binary Number System

A computer is an electronic device and it can understand the switching language only (i.e. a combination of OFF and ON only). The combinations of the circuits can represent numbers, letters, or symbols. How many combinations of can you create with On and Off? It may seem very limited. However, the combinations of the circuits can represent numbers, letters, or symbols – anything digital.

Binary numbers are those whose digits can be 0 or 1 only, and these digits are known as BITs (BInary digiTs). Eight binary digits make up a byte. 

Watch this video to learn more about data representation.

Related Links:

AP CS Principles Curriculum for Schools

AP CS Principles for Students

AP CS Principles Professional Development for Teachers

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