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Questions and Answers
What is the Excess-3 code for the decimal digit 5?
What is the Excess-3 code for the decimal digit 5?
- 1100
- 1000
- 1011 (correct)
- 1001
Which of the following codes is specifically designed to represent decimal digits using exactly two bits set to 1?
Which of the following codes is specifically designed to represent decimal digits using exactly two bits set to 1?
- 2-out-of-5 code (correct)
- Gray code
- Self-Complement code
- Excess-3 code
What is the primary characteristic of Gray code?
What is the primary characteristic of Gray code?
- Every combination differs by two bits
- It has four bits for each decimal digit
- Only one bit differs between successive values (correct)
- It's a weighted code
In a 2-out-of-5 code, how many unique combinations can represent decimal digits?
In a 2-out-of-5 code, how many unique combinations can represent decimal digits?
What is the binary representation of the decimal number 4 in Excess-3 code?
What is the binary representation of the decimal number 4 in Excess-3 code?
Which of the following codes aids in error correction for digital communications?
Which of the following codes aids in error correction for digital communications?
What operation commonly uses a shift count code in programming?
What operation commonly uses a shift count code in programming?
Which code has a property where no digit representation has more than one bit difference?
Which code has a property where no digit representation has more than one bit difference?
What is a characteristic of weighted codes?
What is a characteristic of weighted codes?
Which of the following codes is self-complementing?
Which of the following codes is self-complementing?
How many bits are required in BCD to represent a number with 3 decimal digits?
How many bits are required in BCD to represent a number with 3 decimal digits?
What is the binary representation of the decimal number 185 in BCD?
What is the binary representation of the decimal number 185 in BCD?
Which of the following statements about BCD is correct?
Which of the following statements about BCD is correct?
What defines sequential codes?
What defines sequential codes?
What is the primary function of error detecting and correcting codes?
What is the primary function of error detecting and correcting codes?
Which of the following is NOT a type of digital code?
Which of the following is NOT a type of digital code?
What is the purpose of parity bits in error-detecting codes?
What is the purpose of parity bits in error-detecting codes?
Given the blocks 1011 and 0001, how is the first block expanded to a 7-bit representation?
Given the blocks 1011 and 0001, how is the first block expanded to a 7-bit representation?
How is the parity bit P1 calculated in the 8-bit data structure?
How is the parity bit P1 calculated in the 8-bit data structure?
What does BCD stand for in alphanumeric codes?
What does BCD stand for in alphanumeric codes?
What range of characters can be represented using the standard BCD code?
What range of characters can be represented using the standard BCD code?
In parity bit error detection, if bits 1 and 2 are incorrect, where is the error likely to occur?
In parity bit error detection, if bits 1 and 2 are incorrect, where is the error likely to occur?
What is the characteristic of the minimal bit representation for standard alphanumeric codes?
What is the characteristic of the minimal bit representation for standard alphanumeric codes?
What is the maximum number of characters that can be represented in ASCII code?
What is the maximum number of characters that can be represented in ASCII code?
Which of the following correctly describes the EBCDIC code?
Which of the following correctly describes the EBCDIC code?
Which of the following represents a common error when understanding error detection?
Which of the following represents a common error when understanding error detection?
In ASCII, which bit is considered the parity bit for advancements in error-checking?
In ASCII, which bit is considered the parity bit for advancements in error-checking?
Identify the correct statement regarding the characters represented in EBCDIC code.
Identify the correct statement regarding the characters represented in EBCDIC code.
Which hexadecimal code represents the carriage return (CR) in ASCII?
Which hexadecimal code represents the carriage return (CR) in ASCII?
What does the term 'zone bit' in ASCII refer to?
What does the term 'zone bit' in ASCII refer to?
What character does the binary value 0001 in EBCDIC represent?
What character does the binary value 0001 in EBCDIC represent?
Which of the following correctly describes the difference between EBCDIC and ASCII?
Which of the following correctly describes the difference between EBCDIC and ASCII?
What is a key advantage of using Gray Code in numerical representation?
What is a key advantage of using Gray Code in numerical representation?
Which of the following correctly describes the function of a parity bit?
Which of the following correctly describes the function of a parity bit?
What is the minimum number of parity bits required when encoding a message of 4 data bits using Hamming code?
What is the minimum number of parity bits required when encoding a message of 4 data bits using Hamming code?
How does the addition of multiple parity bits affect communication efficiency?
How does the addition of multiple parity bits affect communication efficiency?
In Hamming code, what does the relationship '$d \geq 5$ and $d \leq 11$' indicate?
In Hamming code, what does the relationship '$d \geq 5$ and $d \leq 11$' indicate?
Which of the following best explains why Hamming code uses even parity?
Which of the following best explains why Hamming code uses even parity?
What does the notation 'p' represent in the context of error-detecting codes?
What does the notation 'p' represent in the context of error-detecting codes?
Which operation is used to convert between Binary and Gray codes?
Which operation is used to convert between Binary and Gray codes?
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Study Notes
Digital Codes: Overview
- Digital data is represented and processed as a group of bits, also known as a binary code.
- Weighted codes: Each digit has a specific weight based on its position.
- Non-weighted codes: Digits are not positionally weighted.
- Reflective codes: The code for a digit is the complement of the code for its inverse (for example, the code for 9 is the inverse of the code for 0).
- Sequential codes: Each code is one binary value higher than the previous code.
- Alphanumeric codes: These represent numbers, alphabet characters, and symbols.
- Error-detecting and correcting codes: Detect errors in data communication and processing.
Numeric Codes
- BCD (Binary Coded Decimal): A number with k decimal digits requires 4k bits.
- Example: Decimal 396 represented in BCD is 0011 1001 0110 (12 bits).
- Each group of 4 bits directly corresponds to one decimal digit.
- The binary combinations 1010 through 1111 are not used in BCD.
- Excess-3 code: BCD code + 0011.
- It also has a self-complementing characteristic.
- Other Non-weighted Codes:
- 2-out-of-5 code: Each decimal digit is represented by 5 bits, with exactly two bits set to 1 and the rest set to 0.
- Shift count code: Describes the number of bit shifts in a binary number. Used for tasks like bit manipulation.
- Gray code: A system where two successive values differ in only one bit. Useful for error detection and analog-to-digital conversion.
Gray Code Properties
- Only one bit changes between successive values.
- Used in Analog to Digital Converters (ADCs) for error detection and reducing power consumption.
Error-Detecting Codes
- Parity: An extra bit (parity bit) is added to make the total number of 1s in a message either even or odd.
- Hamming Code: Uses multiple parity bits to detect and correct single-bit errors.
- Number of bits n needed for error detection/correction is related to the number of data bits d:
- 2 ^(n-1)-n+1 <= d <= 2 ^(n-1)-n-1.
- Example: 4 parity bits are required if you have 5 to 11 data bits.
- Number of bits n needed for error detection/correction is related to the number of data bits d:
Hamming Code Implementation
- Parity bits are placed at positions 1, 2, 4, 8, and so on, depending on the location of the parity.
- Data bits fill the remaining locations.
Alphanumeric Codes
- Standard BCD Code: Expresses one character using 6 bits.
- Maximum of 64 characters can be represented.
- Used in specialized digital systems.
- EBCDIC (Extended Binary Coded Decimal Interchange Code): Uses 8 bits to represent characters.
- ASCII (American Standard Code for Information Interchange):
- Uses 7 bits (128 unique characters) for personal computers, and often 8 bits (with added parity) for communications.
- Each character is divided into a zone bit and a digit bit.
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