Question
Use your Flippy Do to answer the questions.
All 4-Bit Numbers: Fill in the binary equivalents for the decimal numbers below. We’ve started the first three for you.
Binary: 4-bit number
Decimal
Decimal
0000 0 0001 1 0010
2
What do you notice when you compare the odd numbers with the even numbers? What might explain this?
Binary Numbers with exactly one 1: Complete the chart with all 8-bit binary numbers that have exactly one 1. We’ve done the first two for you.
Binary: 8-bit number Decimal
Decimal
(with exactly one 1)
0000 0001 1 0000 0010 2
0000 0100
What do you notice about the decimal equivalents above?
Computer Science Principles
1
Binary: 4-bit number
All 4-Bit Numbers: Fill in the binary equivalents for the decimal numbers below. We’ve started the first three for you.
Binary: 4-bit number
Decimal
Decimal
0000 0 0001 1 0010
2
What do you notice when you compare the odd numbers with the even numbers? What might explain this?
Binary Numbers with exactly one 1: Complete the chart with all 8-bit binary numbers that have exactly one 1. We’ve done the first two for you.
Binary: 8-bit number Decimal
Decimal
(with exactly one 1)
0000 0001 1 0000 0010 2
0000 0100
What do you notice about the decimal equivalents above?
Computer Science Principles
1
Binary: 4-bit number
Answers
GPT-4o mini
Let's fill in the missing parts first.
### 4-Bit Numbers
| Binary | Decimal |
|---------|---------|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
#### Observations
When you compare the odd numbers to the even numbers:
- **Even numbers**: These all have a binary representation that ends in `0`.
- **Odd numbers**: These all have a binary representation that ends in `1`.
This pattern occurs because binary counting is structured such that the least significant bit (the rightmost bit) indicates whether the number is odd or even. A `0` signifies even, while a `1` signifies odd.
---
### 8-Bit Numbers with Exactly One '1'
Next, let's fill in the chart for 8-bit binary numbers that have exactly one `1`.
| Binary | Decimal |
|--------------|---------|
| 0000 0001 | 1 |
| 0000 0010 | 2 |
| 0000 0100 | 4 |
| 0000 1000 | 8 |
| 0001 0000 | 16 |
| 0010 0000 | 32 |
| 0100 0000 | 64 |
| 1000 0000 | 128 |
#### Observations
The decimal equivalents of the binary numbers with exactly one `1` generally follow the pattern of powers of 2:
- The positions of `1` in the binary number correspond to powers of 2.
- The decimal values represent \(2^0\), \(2^1\), \(2^2\), \(2^3\), \(2^4\), \(2^5\), \(2^6\), and \(2^7\) respectively.
Hence, each binary number represents increasing values corresponding to the powers of 2, showing a direct relationship between the positional value of `1` and its decimal equivalent.
### 4-Bit Numbers
| Binary | Decimal |
|---------|---------|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
#### Observations
When you compare the odd numbers to the even numbers:
- **Even numbers**: These all have a binary representation that ends in `0`.
- **Odd numbers**: These all have a binary representation that ends in `1`.
This pattern occurs because binary counting is structured such that the least significant bit (the rightmost bit) indicates whether the number is odd or even. A `0` signifies even, while a `1` signifies odd.
---
### 8-Bit Numbers with Exactly One '1'
Next, let's fill in the chart for 8-bit binary numbers that have exactly one `1`.
| Binary | Decimal |
|--------------|---------|
| 0000 0001 | 1 |
| 0000 0010 | 2 |
| 0000 0100 | 4 |
| 0000 1000 | 8 |
| 0001 0000 | 16 |
| 0010 0000 | 32 |
| 0100 0000 | 64 |
| 1000 0000 | 128 |
#### Observations
The decimal equivalents of the binary numbers with exactly one `1` generally follow the pattern of powers of 2:
- The positions of `1` in the binary number correspond to powers of 2.
- The decimal values represent \(2^0\), \(2^1\), \(2^2\), \(2^3\), \(2^4\), \(2^5\), \(2^6\), and \(2^7\) respectively.
Hence, each binary number represents increasing values corresponding to the powers of 2, showing a direct relationship between the positional value of `1` and its decimal equivalent.