Binary conversion

Number systems · Lesson

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Decimal → binary conversion

Learn the method, study an example, practice with gradually reduced support and check whether you have mastered the skill.

1. How it works

To convert a decimal number to binary, repeatedly divide it by 2 and record each remainder. When the quotient reaches 0, read the remainders from bottom to top.

2. Step-by-step example: 13

1

13 ÷ 2 = 6 remainder 1

2

6 ÷ 2 = 3 remainder 0

3

3 ÷ 2 = 1 remainder 1

4

1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top: 1101

Therefore 13₁₀ = 1101₂.

3. Guided practice

Progress: 0 / 5 exercises — correct: 0

Convert 7 to binary.

4. Learning objective

The goal is not to guess a conversion, but to apply the method independently and explain why the remainders are read from bottom to top.

Continue with binary → decimal →

Your competency map

What you need to know for Decimal → binary

ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.

You can start right away. This is a foundation module: it does not require earlier skills from the learning path.

How to reason about it

Successive division works because every division by 2 separates the quotient from the least significant bit, which is the remainder 0 or 1.

Procedure

Divide the number by 2, record the remainder, continue with the quotient until it reaches 0, then read the remainders from bottom to top.

Common mistakes

The most common mistake is reading the remainders in the order in which they were produced. Remember: the first remainder is the least significant bit.

How to check the result

Convert the binary result back by adding the powers of 2 corresponding to bits equal to 1. You must obtain the starting decimal number.

Editable diagram

Your mind map

Follow the five branches: Rule → Procedure → Worked example → Common mistake → Check. You can drag, reorder and collapse branches while studying; your changes remain saved on this device.

Rule Procedure Example Common mistake Check

Select a node with one click. With “Connect”, select the source node first and then the target node.

From theory to practice

Now try it yourself

You have seen the rule, procedure, example, common mistake and check. Start an exercise on the same topic: ConceptStep guides you at first, then progressively reduces help until you work independently.

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What to remember

Do not memorize only a sequence of steps. Explain the rule aloud, reconstruct the procedure, work through the example, identify the common mistake, and finish with the check. If you can follow these five branches without looking, you are ready for independent practice.

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