Question

Световое табло состоит из лампочек, каждая из которых может находиться в двух состояниях: "Включено" или "выключено". Какое наименьшее количество лампочек должно находиться на табло, чтобы с его помощью можно было передавать 15 различных сигналов? Информатика 8-ой класс.

Answer 1

4лааааааааааааампочкиии

Answer 2

Minimum Number of Light Bulbs Required for 15 Different Signals

To transmit 15 different signals using a light board with bulbs that can be either "on" or "off," we need to determine the minimum number of bulbs required.

To solve this problem, we can use the concept of binary numbers. Since each bulb can be in one of two states (on or off), we can represent each signal as a binary number. The number of bulbs required will be equal to the number of digits needed to represent 15 in binary.

To convert 15 to binary, we can use the following steps: 1. Divide 15 by 2 and note the remainder: 15 ÷ 2 = 7 remainder 1. 2. Divide the quotient from step 1 by 2 and note the remainder: 7 ÷ 2 = 3 remainder 1. 3. Repeat step 2 until the quotient is 0: 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1.

The remainders in reverse order give us the binary representation of 15: 1111.

Therefore, we need a minimum of 4 light bulbs to transmit 15 different signals on the light board.

Explanation

Each bulb can represent a binary digit (0 or 1). With 4 bulbs, we can represent all possible combinations of 4 binary digits, which range from 0000 to 1111. This allows us to represent a total of 16 different signals (including 0). Since we only need to transmit 15 different signals, 4 bulbs are sufficient.

Example

To illustrate how the 4 bulbs can represent 15 different signals, we can assign each bulb to a binary digit position (from left to right: bulb 1, bulb 2, bulb 3, bulb 4). The "on" state of a bulb represents a binary digit of 1, and the "off" state represents a binary digit of 0.

Here is a table showing the binary representation of numbers from 0 to 15 using the 4 bulbs:

| Number | Binary Representation | |--------|----------------------| | 0 | 0000 | | 1 | 0001 | | 2 | 0010 | | 3 | 0011 | | 4 | 0100 | | 5 | 0101 | | 6 | 0110 | | 7 | 0111 | | 8 | 1000 | | 9 | 1001 | | 10 | 1010 | | 11 | 1011 | | 12 | 1100 | | 13 | 1101 | | 14 | 1110 | | 15 | 1111 |

As you can see, all 15 different signals can be represented using the 4 bulbs.

Conclusion

To transmit 15 different signals using a light board with bulbs that can be either "on" or "off," a minimum of 4 light bulbs is required. Each bulb represents a binary digit, and the binary representation of 15 is 1111. With 4 bulbs, we can represent all possible combinations of 4 binary digits, allowing us to transmit 15 different signals.