DECMATRIX

Mathematical Tools

Base Conversion Exercises

Convert integers from 0 to 255 between four bases. Choose a pair or mix the bases, check your answer and move on when you are ready.

Settings apply to the next new exercise. Retry keeps the current challenge.

Unaided correct:
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Errors:
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Explore freely in the base converter

How to practise

Start an exercise, read the source and target bases and enter your answer. Choose Check to test your reasoning. A wrong answer keeps the question for another attempt; a new challenge only appears when you choose an action.

Counters apply to this session. Each distinct wrong answer counts once per challenge; checking the same answer again does not add errors. Using a hint or revealing the solution marks the exercise as assisted. Retry starts a fresh attempt at the same challenge.

What does the base mean?

The base determines the available digits and the weight of each position. Binary uses 0 and 1; octal uses 0 to 7; decimal uses 0 to 9; hexadecimal uses 0 to 9 and A to F. From right to left, the weights are base⁰, base¹, base² and so on.

Independent worked examples

Decimal 10 = binary 1010, because 10 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰. In reverse, binary 1010 = decimal 10.

Hexadecimal FF = decimal 255, because 15×16 + 15 = 255. Decimal 64 = octal 100, because 1×8² = 64. These are separate teaching examples, not an automatic solution to the active challenge.

Common mistakes

Do not confuse decimal 10 with binary 10. The digit 2 is not binary, and 8 is not octal. Do not use 0b/0x prefixes or separators inside a number. Hexadecimal letters may be uppercase or lowercase.

Exercises only use nonnegative integers from 0 to 255, without precision loss in this range. The whole answer is validated: a valid prefix followed by invalid characters is not accepted.

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