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Beginner Topic 1 of 51 Math for Computing

Number Systems

Naturals, integers, rationals and reals.

How it works

A number system is a way of representing numbers with symbols. Positional systems such as decimal (base 10), binary (base 2), octal and hexadecimal give each digit a value that depends on its place, a power of the base. Number sets nest: natural numbers, integers, rationals, reals and complex numbers, each extending the previous to allow new operations such as subtraction, division, limits and square roots of negatives. Converting between bases uses repeated division and place-value expansion.

Where it is used

Computers use binary and hexadecimal for storage and addresses, programmers choose among integer, floating-point and arbitrary-precision types, and mathematics relies on the real and complex fields.

Common pitfall

Mixing up bases when reading numbers, such as treating 10 binary as ten, is common. Computers represent only a finite subset of integers and reals, so overflow and rounding appear. Irrational numbers have no finite decimal expansion, so computed values are approximations. State the base and the type, and know the limits of the representation you use.

Where it fits in the course

Number Systems is topic 1 of 51 in Math for Computing, rated Beginner. It is the first topic in this area. The next topic is Algebra Review.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Math for Computing quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Number Systems?
Naturals, integers, rationals and reals. It belongs to Math for Computing and is a beginner-level topic.
Where do people use Number Systems?
Computers use binary and hexadecimal for storage and addresses, programmers choose among integer, floating-point and arbitrary-precision types, and mathematics relies on the real and complex fields.
What is the most common mistake with Number Systems?
Mixing up bases when reading numbers, such as treating 10 binary as ten, is common.
What should I learn before this topic?
Nothing earlier in Math for Computing is required. This is where the area begins.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Math for Computing quiz.
Is Number Systems hard to learn?
It is a Beginner topic, so it works as an entry point. If the terms are new, read the explanation twice and try the visualizer before the quiz.
How long does it take to learn Number Systems?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Number Systems?
Algebra Review, Exponents and Logarithms, Summations and Series are closely connected. The full list is in the related topics section of this page.
What should I study after Number Systems?
Continue with Algebra Review, the next topic in Math for Computing.

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