computer science

Real data type

Real data type is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Real data type rather than just read about it. In short: A real data type is a data type used in a computer program to represent an approximation of a real number. Because the real numbers are not countable, computers cannot represent them exactly using a finite amount of information.

Key takeaways

Real data type belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Real data type to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Real data type from memory before moving on to harder problems.

Reference excerpt

A real data type is a data type used in a computer program to represent an approximation of a real number. Because the real numbers are not countable, computers cannot represent them exactly using a finite amount of information. Most often, a computer will use a rational approximation to a real number.

Rational numbers

The most general data type for a rational number (a number that can be expressed as a fraction) stores the numerator and the denominator as integers. For example 1/3, which can be calculated to any desired precision. Rational numbers are used, for example, in Interpress from Xerox Corporation.

Fixed-point numbers

A fixed-point data type uses the same, implied, denominator for all numbers. The denominator is usually a power of two. For example, in a hypothetical fixed-point system that uses the denominator 65,536 (216), the hexadecimal number 0x12345678 (0x1234.5678 with sixteen fractional bits to the right of the assumed radix point) means 0x12345678/65536 or 305419896/65536, 4660 + the fractional value 22136/65536, or about 4660.33777. An integer is a fixed-point number with a fractional part of zero.

Floating-point numbers

A floating-point data type is a compromise between the flexibility of a general rational number data type and the speed of fixed-point arithmetic. It uses some of the bits in the data type to specify an exponent for the denominator, today usually power of two although both ten and sixteen have been used.

Decimal numbers

The decimal type is similar to fixed-point or floating-point data type, but with a denominator that is a power of 10 instead of a power of 2.

See also Binary number Decimal number Hexadecimal number IEEE Standard for Floating-Point Arithmetic

References

Worked examples

Example 1 — a first encounter with Real data type

Start with the simplest possible case. Write down what Real data type claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Real data type before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Real data type ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Real data type

In research: Real data type appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Real data type in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Real data type is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer arithmetic, Data types, so understanding it makes those chapters shorter.
In everyday life: Look for Real data type outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Real data type in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Real data type means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Real data type out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Real data type in simple terms?

Why does Real data type matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Real data type?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Real data type.