Binary Worksheets - Worksheet 1: Binary Numbers Represent each ... - Free Printable

Problem Description:

The task involves converting decimal numbers into binary representations using a set of cards. Each card represents a power of 2 (from \(2^0\) to \(2^4\)), and the goal is to select the appropriate cards to represent the given decimal number. The selected cards are marked with dots, while the unused cards are crossed out. Finally, the binary representation is written in the "Binary Number" column.

Solution Approach:

1. Understand the Cards:
- Each card represents a power of 2:
- Card 1: \(2^0 = 1\)
- Card 2: \(2^1 = 2\)
- Card 3: \(2^2 = 4\)
- Card 4: \(2^3 = 8\)
- Card 5: \(2^4 = 16\)

2. Convert Decimal to Binary:
- For each decimal number, determine which powers of 2 sum up to that number.
- Mark the corresponding cards with dots and cross out the unused cards.
- Write the binary representation, where each position corresponds to whether the card is used (1) or not used (0).

3. Steps for Each Number:
- Number 2:
- Binary: \(00010\)
- Explanation: \(2 = 2^1\). Use Card 2 (value 2), and cross out all others.
- Number 5:
- Binary: \(00101\)
- Explanation: \(5 = 2^2 + 2^0 = 4 + 1\). Use Cards 3 and 1, and cross out the rest.
- Number 3:
- Binary: \(00011\)
- Explanation: \(3 = 2^1 + 2^0 = 2 + 1\). Use Cards 2 and 1, and cross out the rest.
- Number 12:
- Binary: \(01100\)
- Explanation: \(12 = 2^3 + 2^2 = 8 + 4\). Use Cards 4 and 3, and cross out the rest.
- Number 19:
- Binary: \(10011\)
- Explanation: \(19 = 2^4 + 2^1 + 2^0 = 16 + 2 + 1\). Use Cards 5, 2, and 1, and cross out the rest.
- Number 8:
- Binary: \(01000\)
- Explanation: \(8 = 2^3\). Use Card 4, and cross out the rest.
- Number 15:
- Binary: \(01111\)
- Explanation: \(15 = 2^3 + 2^2 + 2^1 + 2^0 = 8 + 4 + 2 + 1\). Use Cards 4, 3, 2, and 1, and cross out Card 5.

Final Answer:

The binary representations and card selections are already filled in the worksheet. Here is a summary:

| Number | Cards Used (Dots) | Binary Number |
|--------|-------------------|---------------|
| 2 | Card 2 | 00010 |
| 5 | Cards 3 and 1 | 00101 |
| 3 | Cards 2 and 1 | 00011 |
| 12 | Cards 4 and 3 | 01100 |
| 19 | Cards 5, 2, and 1 | 10011 |
| 8 | Card 4 | 01000 |
| 15 | Cards 4, 3, 2, and 1 | 01111 |

Thus, the final answer is:

\boxed{00010, 00101, 00011, 01100, 10011, 01000, 01111}