CAT Base systems Questions

A positional number system assigns each digit a value according to its position and the base. Conversion questions use powers of the base and restrictions on the digits that can appear.

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Key concepts

Place values and base expansion
Allowed digits
Conversion between bases

CAT base systems practice questions

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Practise Free Tests on InsideIIM

Common mistakes

Using a digit whose value is equal to or greater than the base.
Reading a non-decimal representation as a decimal number.

Practical solving approaches

Expand a representation as a sum of digits multiplied by powers of the base.
Convert through decimal or use repeated division, then verify by expanding the result.

Base systems FAQs

Which digits are valid in base b?: For an integer base b greater than one, digit values run from zero through b − 1.

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CAT Base systems Questions

A positional number system assigns each digit a value according to its position and the base. Conversion questions use powers of the base and restrictions on the digits that can appear.

2 free practice questions

Key concepts

Place values and base expansion
Allowed digits
Conversion between bases

CAT base systems practice questions

Question 1Multiple choiceEASY

Select the correct alternative from the given choices.

Answer the questions independently of each other.

If the base for writing numbers were two, instead of ten, the number 18 would be written as:

Question 2Type in the answerMEDIUM

Enter your response (as an integer) using the virtual keyboard in the box provided.

There are 100 bottles of a drink, out of which only one bottle is poisoned. Anyone who tastes the drink from the
poisoned bottle would die in one hour. However, there is no harm if the drink from other bottles is tasted. A test is
to be conducted using rats to identify the poisoned bottle. What is the minimum number of rats needed for the
test if the poisoned bottle is to be identified in exactly one hour time? Assume that the time taken by the rats to
drink the contents of the bottle is negligible and that rats can drink the contents of as many bottles as we make
them to drink.

Practise Free Tests on InsideIIM

Common mistakes

Using a digit whose value is equal to or greater than the base.
Reading a non-decimal representation as a decimal number.

Practical solving approaches

Expand a representation as a sum of digits multiplied by powers of the base.
Convert through decimal or use repeated division, then verify by expanding the result.

Base systems FAQs

Which digits are valid in base b?: For an integer base b greater than one, digit values run from zero through b − 1.

More Number Systems practice

CAT Base systems Questions

A positional number system assigns each digit a value according to its position and the base. Conversion questions use powers of the base and restrictions on the digits that can appear.

Loading question count…

Key concepts

Place values and base expansion
Allowed digits
Conversion between bases

CAT base systems practice questions

Loading questions…

Practise Free Tests on InsideIIM

Common mistakes

Using a digit whose value is equal to or greater than the base.
Reading a non-decimal representation as a decimal number.

Practical solving approaches

Expand a representation as a sum of digits multiplied by powers of the base.
Convert through decimal or use repeated division, then verify by expanding the result.

Base systems FAQs

Which digits are valid in base b?: For an integer base b greater than one, digit values run from zero through b − 1.

Loading practice data…

CAT Base systems Questions | InsideIIM

CAT Base systems Questions

A positional number system assigns each digit a value according to its position and the base. Conversion questions use powers of the base and restrictions on the digits that can appear.

2 free practice questions

Key concepts

Place values and base expansion
Allowed digits
Conversion between bases

CAT base systems practice questions

Question 1Multiple choiceEASY

Select the correct alternative from the given choices.

Answer the questions independently of each other.

If the base for writing numbers were two, instead of ten, the number 18 would be written as:

Question 2Type in the answerMEDIUM

Enter your response (as an integer) using the virtual keyboard in the box provided.

Practise Free Tests on InsideIIM

Common mistakes

Using a digit whose value is equal to or greater than the base.
Reading a non-decimal representation as a decimal number.

Practical solving approaches

Expand a representation as a sum of digits multiplied by powers of the base.
Convert through decimal or use repeated division, then verify by expanding the result.

Base systems FAQs

Which digits are valid in base b?: For an integer base b greater than one, digit values run from zero through b − 1.

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CAT Base systems Questions

Key concepts

CAT base systems practice questions

Common mistakes

Practical solving approaches

Base systems FAQs

CAT Base systems Questions

Key concepts

CAT base systems practice questions

Common mistakes

Practical solving approaches

Base systems FAQs

More Number Systems practice

CAT Base systems Questions

Key concepts

CAT base systems practice questions

Common mistakes

Practical solving approaches

Base systems FAQs

CAT Base systems Questions

Key concepts

CAT base systems practice questions

Common mistakes

Practical solving approaches

Base systems FAQs

More Number Systems practice