a binary code uses 10 bits to represent each of the 10 decimal digits. each digit is assigned a code of nine 0's and a 1. the code for digit 6, for example is 0001000000. determine the binary code for the remaining decimal digits

This type of binary code is called a "1-out-of-10" code. In this system, each digit (from 0 to 9) is represented by a 10-bit binary number, where one bit is set to 1, and all the other bits are set to 0. The position of the 1 corresponds to the digit's value.

The binary codes for the decimal digits 0 through 9 are:

- **0** → 1000000000
- **1** → 0100000000
- **2** → 0010000000
- **3** → 0001000000
- **4** → 0000100000
- **5** → 0000010000
- **6** → 0000001000 (already provided)
- **7** → 0000000100
- **8** → 0000000010
- **9** → 0000000001

In this way, each decimal digit is represented by a 10-bit binary number with a single 1, corresponding to its position.

Would you like more details on binary encoding systems, or do you have any further questions?

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Here are five follow-up questions for further exploration:

1. How would this system work if we needed to represent more than 10 digits, for example, hexadecimal digits?
2. What are other types of binary codes used in digital systems (e.g., Gray code or BCD)?
3. Can you explain how binary numbers are used in computers for arithmetic operations?
4. How would you convert these binary codes back into decimal digits?
5. What is the difference between "1-out-of-10" code and other positional binary systems?

**Tip:** In digital systems, binary encoding techniques optimize data storage and transmission, especially in applications like error detection and correction.

A binary code uses 10 bits to represent each of the 10 decimal digits. Each digit is assigned a code of nine 0's and a 1. The code for digit 6, for example, is 0001000000. Determine the binary code for the remaining decimal digits.

Explore how to represent decimal digits using 10-bit binary codes in a 1-out-of-10 system. This problem explains how each digit from 0 to 9 is encoded using a 10-bit sequence, with one bit set to 1 and the rest as 0. Suitable for high school students learning digital systems.

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