Question

Comprehension:

In a certain number system there are only two notations to represent numbers: ▵ and β .

0 is represented by ▵ and 1 by β. The subsequent numbers are represented in the following manner:

2 is represented as β▵.

3 is represented as ββ,
4 is represented as β▵▵,

5 is represented as β▵β and so on.

How will you represent 81 in the given number system?

• A. β▵▵β▵β▵
• B. β▵β▵β▵β
• C. β▵β▵▵ββ
• D. β▵β▵▵▵β

Answer 1

Answer:

D. β▵β▵▵▵β

The given number system is binary with different symbols:

• ▵ = 0

• β = 1

Examples confirm this:

• 0 = ▵

• 1 = β

• 2 = β▵ (binary 10)

• 3 = ββ (binary 11)

• 4 = β▵▵ (binary 100)

• 5 = β▵β (binary 101)

Step 1: Convert 81 to binary

81 = 64 + 16 + 1

So,

81 = 1010001₂

Step 2: Replace binary digits with the given symbols

• 1 → β

• 0 → ▵

1010001 → β▵β▵▵▵β

Answer: β▵β▵▵▵β