Grade 10 ICT worksheet focusing on converting decimal numbers to binary and octal systems.

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 from bottom to top: 11101₂

✔ So, the correct answer is: (iii) 11101₂

> Note: Option (ii) appears twice. Likely a typo in the worksheet. Assuming options are:
> - (i) 10000₂
> - (ii) 10101₂
> - (iii) 11101₂
> - (iv) 11111₂

So, Answer: (iii) 11101₂

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Question 2:

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

Convert 156₁₀ to octal using repeated division by 8:

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

Read remainders from bottom to top: 234₈

✔ So, the correct answer is: (ii) 234₈

> Options:
> - (i) 121₈
> - (ii) 234₈
> - (iii) 574₈
> - (iv) 770₈

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
```

Read remainders: 62₈

✔ So, the correct answer is: (i) 62₈

> Options:
> - (i) 62₈
> - (ii) 72₈
> - (iii) 82₈
> - (iv) 92₈

Answer: (i) 62₈

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Question 4:

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

Wait — this says "decimal equivalent of decimal 50"? That doesn't make sense.

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

- (i) 110000₂
- (ii) 110010₂
- (iii) 110110₂
- (iv) 111010₂

And it says: "the decimal equivalent of decimal 50" — that seems like a typo.

It should probably be: "Which of the following is the binary equivalent of decimal 50?"

Because otherwise, "decimal equivalent of decimal 50" is just 50.

But since the options are binary, we assume it’s asking for binary equivalent of 50₁₀.

Let’s 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 → 110010₂

✔ So, the 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?

This is confusing: “decimal equivalent of decimal 612”?

That would just be 612, but the options are binary numbers.

Looking at the options:

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

Wait — it says: "decimal equivalent of decimal 612₁₀" — again, that’s redundant.

But likely, it means: "Which of the following is the binary equivalent of decimal 612₁₀?"

So 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 write remainders from bottom to top:

1001100100₂

✔ So, the binary equivalent is 1001100100₂

Now check options:

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

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

Assuming option (iv) is correct with proper notation.

But note: (ii) is written as 1001100100 without subscript, while (iv) has 1001100100₂

So, the correct choice is: (iv) 1001100100₂

Answer: (iv) 1001100100₂

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✔ Final Answers:

| Question | Correct Answer |
|--------|----------------|
| 1 | (iii) 11101₂ |
| 2 | (ii) 234₈ |
| 3 | (i) 62₈ |
| 4 | (ii) 110010₂ |
| 5 | (iv) 1001100100₂ |

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📝 Summary of Conversions:

1. 29₁₀ → 11101₂
2. 156₁₀ → 234₈
3. 50₁₀ → 62₈
4. 50₁₀ → 110010₂
5. 612₁₀ → 1001100100₂

These conversions follow standard methods:
- Decimal to Binary: Repeated division by 2.
- Decimal to Octal: Repeated division by 8.
- Binary to Decimal: Sum of powers of 2.

Let me know if you'd like a visual explanation or table!