Grade 10 ICT worksheet focusing on converting decimal numbers to binary and octal systems, with five multiple-choice questions.

Let's solve each question step by step from the Grade 10 ICT Evaluation Worksheet on converting between decimal, binary, and octal number systems.

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Question 1:

Which of the following is the binary equivalent of decimal 29₁₀?

We convert 29₁₀ to binary using repeated division by 2:

- 29 ÷ 2 = 14 remainder 1
- 14 ÷ 2 = 7 remainder 0
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1

Now read the remainders bottom to top:
→ 11101₂

So, correct answer is: (iii) 11101₂

✔ Answer: (iii) 11101₂

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Question 2:

Which of the following is the octal equivalent of decimal 156₁₀?

Convert 156₁₀ to octal (base 8) using repeated division by 8:

- 156 ÷ 8 = 19 remainder 4
- 19 ÷ 8 = 2 remainder 3
- 2 ÷ 8 = 0 remainder 2

Read remainders bottom to top: 234₈

✔ Answer: (ii) 234₈

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Question 3:

Which of the following is the octal equivalent of decimal 50?

Convert 50₁₀ to octal:

- 50 ÷ 8 = 6 remainder 2
- 6 ÷ 8 = 0 remainder 6

So, 62₈

✔ Answer: (i) 62₈

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Question 4:

Which of the following is the decimal equivalent of binary 110010₂?

Wait — the question says: "decimal equivalent of decimal 50"? That seems like a typo.

But looking at the options: all are binary numbers, so likely it meant:

> "Which of the following is the binary equivalent of decimal 50?"

Because otherwise, asking for the decimal equivalent of decimal 50 is trivial (it's 50).

Let’s assume it's asking:
"Which of the following is the binary equivalent of decimal 50?"

Convert 50₁₀ to binary:

- 50 ÷ 2 = 25 r 0
- 25 ÷ 2 = 12 r 1
- 12 ÷ 2 = 6 r 0
- 6 ÷ 2 = 3 r 0
- 3 ÷ 2 = 1 r 1
- 1 ÷ 2 = 0 r 1

Remainders: 110010₂

So, correct answer is: (ii) 110010₂

✔ Answer: (ii) 110010₂

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Question 5:

Which of the following is the decimal equivalent of decimal 612₁₀?

Wait — this is confusing. It says:
> "Which of the following is the decimal equivalent of decimal 612₁₀?"

That makes no sense — the decimal equivalent of a decimal number is itself.

But looking at the options: they are all binary numbers.

So likely, the question is:
> "Which of the following is the binary equivalent of decimal 612₁₀?"

Let’s convert 612₁₀ to binary:

Use repeated division by 2:

- 612 ÷ 2 = 306 r 0
- 306 ÷ 2 = 153 r 0
- 153 ÷ 2 = 76 r 1
- 76 ÷ 2 = 38 r 0
- 38 ÷ 2 = 19 r 0
- 19 ÷ 2 = 9 r 1
- 9 ÷ 2 = 4 r 1
- 4 ÷ 2 = 2 r 0
- 2 ÷ 2 = 1 r 0
- 1 ÷ 2 = 0 r 1

Now read remainders bottom to top:
1001100100₂

Check:
Options are:

(i) 1101100101
(ii) 1001100100
(iii) 1101100101
(iv) 1001100100₂

So both (ii) and (iv) are 1001100100, but (iv) has subscript 2 → correct notation.

So correct answer is: (iv) 1001100100₂

✔ Answer: (iv) 1001100100₂

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✔ Final Answers:

1. (iii) 11101₂
2. (ii) 234₈
3. (i) 62₈
4. (ii) 110010₂
5. (iv) 1001100100₂

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🔍 Explanation Summary:

- Binary conversion: Divide by 2 repeatedly, collect remainders.
- Octal conversion: Divide by 8 repeatedly, collect remainders.
- Always read remainders from bottom to top.
- Binary to decimal: Use place values (powers of 2).
- Decimal to binary: Repeated division by 2.
- Octal uses base 8; each digit represents 3 bits.

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