Binary, Decimal and Hexadecimal Number Systems
Khan Academy・2 minutes read
The text explores representing clusters of objects in different number systems, such as base ten, base two, and base 16. It demonstrates how different bases represent the same cluster of objects through grouping and individual values.
Insights
- In base ten, 35 objects are represented as three tens and five ones, illustrating the concept of grouping objects based on powers of ten.
- Transitioning to base two and base 16 showcases the versatility of number systems, highlighting how different bases offer unique ways to represent the same quantity of objects through varied groupings and digit symbols.
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Recent questions
What is the base ten system?
A numerical system with ten unique digits.
How is base two represented?
Using only the digits 0 and 1.
What is the hexadecimal system?
A base 16 numerical system.
How are objects divided in base ten?
Into groups of ten and individual objects.
What is the largest power in base two for 35?
32.
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Summary
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Representing Clusters in Different Number Systems
- The text discusses representing clusters of objects in different number systems.
- Initially, the base ten system is explained, where the largest power of ten fitting into the cluster of 35 objects is 10.
- Dividing the objects into groups of ten, it results in three groups of ten and five individual objects.
- In base ten, this is represented as three tens and five ones, totaling 35.
- Moving to base two, the largest power of two fitting into 35 is 32.
- Dividing the objects accordingly, it results in one group of 32, one group of two, and one individual object.
- In base two, this is represented as 100011, equating to 35.
- The text then delves into base 16, the hexadecimal system, with 16 unique digits.
- Dividing the 35 objects, it results in two groups of 16 and three individual objects.
- In base 16, this is represented as 23, signifying two sixteens and three ones, totaling 35.
