Math Problem Statement
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
Solution
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?
Here are five follow-up questions for further exploration:
- How would this system work if we needed to represent more than 10 digits, for example, hexadecimal digits?
- What are other types of binary codes used in digital systems (e.g., Gray code or BCD)?
- Can you explain how binary numbers are used in computers for arithmetic operations?
- How would you convert these binary codes back into decimal digits?
- 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.
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Math Problem Analysis
Mathematical Concepts
Binary Representation
Digital Encoding
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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