Enter a player name to begin or load your saved progress.
A fundamental characteristic of a reflected binary code is that any two successive values differ in precisely one bit.
Answer: True
Explanation: The definition of a reflected binary code, also known as Gray code, states that any two successive values in its sequence differ by only one binary digit.
In the natural binary numeral system, the transition from decimal 1 (001) to 2 (010) necessitates a change in only one bit, analogous to Gray code.
Answer: False
Explanation: In natural binary, the transition from decimal 1 (001) to 2 (010) requires two bits to change (the first and second bits). Gray code, however, ensures only one bit changes between successive values.
Codes in which adjacent code words differ by precisely one symbol are exclusively designated as Gray codes.
Answer: False
Explanation: Codes where adjacent code words differ by exactly one symbol are also known by several other terms, including unit-distance, single-distance, single-step, monostrophic, or syncopic codes, not exclusively Gray codes.
In standard Gray code encoding, the least significant bit adheres to a repetitive pattern of 4 'on' states followed by 4 'off' states.
Answer: False
Explanation: In standard Gray code encoding, the least significant bit follows a repetitive pattern of 2 on, 2 off. The next digit follows a pattern of 4 on, 4 off.
The cyclic property of Gray code implies that the final entry differs from the initial entry by only one bit change, thereby enabling seamless transitions.
Answer: True
Explanation: The cyclic property of Gray code ensures that the last entry differs from the first entry by only one bit change, which is essential for seamless transitions when cycling through all possible states.
One of the five principal properties of the standard reflecting Gray code is that each entry differs by precisely one bit from the preceding entry.
Answer: True
Explanation: One of the five key properties of the standard reflecting Gray code is indeed that each entry differs by only one bit from the previous entry, maintaining a Hamming distance of 1.
The table titled 'Gray code' illustrates the decimal values from 0 to 15 and their corresponding 4-bit Gray code representations.
Answer: True
Explanation: The table titled 'Gray code' illustrates the decimal values from 0 to 15 and their corresponding 4-bit Gray code representations, highlighting the single-bit change property.
What is the defining characteristic of a reflected binary code?
Answer: Only one binary digit changes between consecutive numbers.
Explanation: The fundamental characteristic of a reflected binary code, or Gray code, is that any two successive values differ in only one bit.
In the standard encoding of Gray code, what is the repetitive pattern of the least significant bit?
Answer: 2 on, 2 off
Explanation: In the standard encoding of the Gray code, the least significant bit follows a repetitive pattern of 2 on, 2 off.
What is the cyclic or adjacency property of Gray code?
Answer: The last entry differs from the first entry by only one switch change.
Explanation: The cyclic property of Gray code means that for a given n-bit code, the last entry differs from the first entry by only one switch change, allowing for seamless transitions.
Frank Gray formally introduced the term 'reflected binary code' in his 1947 patent application.
Answer: True
Explanation: Frank Gray, a Bell Labs researcher, introduced the term 'reflected binary code' in his 1947 patent application.
The binary-reflected Gray code (BRGC) was named due to its construction from conventional binary code through a process of 'inversion'.
Answer: False
Explanation: The binary-reflected Gray code (BRGC) was named because it can be built up from the conventional binary code by a 'reflection process,' not an 'inversion' process.
Gray code is occasionally erroneously attributed to Elisha Gray, a 19th-century inventor.
Answer: True
Explanation: The Gray code is sometimes incorrectly attributed to Elisha Gray, a 19th-century electrical device inventor, rather than Frank Gray, after whom it is named.
Émile Baudot and Otto Schäffler employed a 5-unit reflected binary code in early telegraphy systems during the late 19th century.
Answer: True
Explanation: Émile Baudot and Otto Schäffler both utilized a 5-unit reflected binary code in their respective printing telegraph systems in the mid-1870s.
Frank Gray's principal motivation for his research on reflected binary codes was to enhance data storage efficiency in nascent computing systems.
Answer: False
Explanation: Frank Gray's primary motivation was to minimize errors during the conversion of analog signals to digital signals, not to improve data storage efficiency in early computers.
George R. Stibitz employed a reflected binary code in a binary pulse counting device in 1941.
Answer: True
Explanation: George R. Stibitz utilized a reflected binary code in a binary pulse counting device as early as 1941, demonstrating an early practical application of this coding scheme.
The image caption 'Gray's patent introduces the term "reflected binary code"' signifies that Frank Gray's patent was the inaugural formal introduction of this terminology.
Answer: True
Explanation: The image caption confirms that Frank Gray's patent document was the first place where the term 'reflected binary code' was formally introduced.
Who introduced the term 'reflected binary code' in a 1947 patent application?
Answer: Frank Gray
Explanation: Frank Gray, a Bell Labs researcher, introduced the term 'reflected binary code' in his 1947 patent application.
How does the binary-reflected Gray code (BRGC) get its name?
Answer: It is derived from conventional binary code by a 'reflection process'.
Explanation: Frank Gray derived the name 'reflected binary code' from the fact that it 'may be built up from the conventional binary code by a sort of reflection process'.
Which 19th-century inventor is Gray code sometimes incorrectly attributed to?
Answer: Elisha Gray
Explanation: The Gray code is sometimes incorrectly attributed to Elisha Gray, a 19th-century electrical device inventor, rather than Frank Gray.
What was Frank Gray's primary motivation for inventing a method to convert analog signals to reflected binary code groups?
Answer: To minimize errors during analog-to-digital conversion.
Explanation: Frank Gray's primary motivation was to minimize errors during the conversion of analog signals to digital signals, for which his vacuum tube-based apparatus was designed.
Who utilized a reflected binary code in a binary pulse counting device as early as 1941?
Answer: George R. Stibitz
Explanation: George R. Stibitz utilized a reflected binary code in a binary pulse counting device as early as 1941.
Gray codes are primarily employed to augment the complexity of logic operations within digital systems.
Answer: False
Explanation: Gray codes are primarily used to simplify logic operations and reduce errors in digital systems, not to increase complexity.
The issue with natural binary codes in position-indicating devices is that all physical switches transition states perfectly synchronously, thereby leading to false readings.
Answer: False
Explanation: The problem with natural binary codes in position-indicating devices is precisely that physical switches *do not* change states perfectly in synchrony, which can lead to brief, spurious readings and false values.
The unit-distance property of Gray codes prevents the storage of false values by sequential systems by ensuring that only one switch changes state at any given time.
Answer: True
Explanation: The unit-distance property of Gray codes ensures that only one switch changes state during transitions, eliminating ambiguity and preventing sequential systems from storing false values.
Gray codes enhance error correction in Quadrature Amplitude Modulation (QAM) by ensuring that adjacent constellation points differ by multiple bits, thereby increasing error detectability.
Answer: False
Explanation: Gray codes enhance error correction in QAM by arranging constellation points so that adjacent bit patterns differ by *only one bit*, making single-bit transmission errors correctable.
Position encoders utilize Gray codes to prevent misreads by ensuring that multiple bits change simultaneously between adjacent positions.
Answer: False
Explanation: Position encoders use Gray codes to prevent misreads by ensuring *only one bit* changes between consecutive positions, thereby limiting the maximum position error.
Gray codes are occasionally employed in genetic algorithms because mutations typically result in drastic, non-incremental changes.
Answer: False
Explanation: Gray codes are used in genetic algorithms because mutations in the code typically lead to *incremental* changes, although a single bit-change can occasionally cause a significant shift.
Gray codes are employed for labeling the axes of Karnaugh maps in Boolean circuit minimization.
Answer: True
Explanation: Gray codes are used in labeling the axes of Karnaugh maps, a graphical method for logic circuit minimization, and also in Händler circle graphs for the same purpose.
Digital logic designers employ Gray codes for transmitting multi-bit count information between disparate clock domains with the deliberate intention of capturing invalid transient states.
Answer: False
Explanation: Digital logic designers use Gray codes for passing multi-bit count information between different clock domains to *prevent* invalid transient states from being captured, ensuring data integrity.
Gray code counters are employed in FIFO buffers to ensure that invalid transient states are captured when count information traverses clock domains.
Answer: False
Explanation: Gray code counters are used in FIFO buffers to *prevent* invalid transient states from being captured when count information crosses clock domains, thereby ensuring data integrity.
Gray codes reduce CPU power consumption in low-power designs by augmenting the number of state changes of address bits during memory access.
Answer: False
Explanation: Gray codes reduce CPU power consumption in low-power designs by *significantly reducing* the number of state changes of the address bits during memory access, not increasing them.
Single-track Gray codes (STGCs) necessitate multiple tracks, thereby increasing manufacturing cost and physical dimensions for rotary encoders.
Answer: False
Explanation: Single-track Gray codes (STGCs) offer advantages in rotary encoder fabrication because their *single-track nature* reduces manufacturing cost and size compared to multi-track codes.
Which of the following is a primary practical application of Gray codes?
Answer: Facilitating error correction in digital communications.
Explanation: Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications.
What problem do natural binary codes pose for electromechanical switches indicating position?
Answer: They can lead to brief, spurious readings when multiple bits change at different times.
Explanation: Natural binary codes can lead to brief, spurious readings in position-indicating devices because physical switches do not change states perfectly in synchrony, causing multiple bits to change at slightly different times.
How do Gray codes enhance error correction in Quadrature Amplitude Modulation (QAM)?
Answer: By arranging constellation points so adjacent bit patterns differ by only one bit.
Explanation: In QAM, Gray codes arrange constellation points so that bit patterns of adjacent points differ by only one bit, which, combined with forward error correction, helps correct single-bit transmission errors.
How do position encoders leverage Gray codes to prevent measurement errors?
Answer: By limiting the maximum position error to a small, adjacent value due to single-bit changes.
Explanation: Position encoders use Gray codes to prevent misreads by ensuring only one bit changes between consecutive positions, thereby limiting the maximum position error to a small, adjacent value.
For what purpose are Gray codes used in Boolean circuit minimization?
Answer: To label the axes of Karnaugh maps.
Explanation: Gray codes are used in labeling the axes of Karnaugh maps, a graphical method for logic circuit minimization.
What is the primary benefit of using Gray codes for passing multi-bit count information between different clock domains?
Answer: It prevents invalid transient states from being captured.
Explanation: Gray codes are used for passing multi-bit count information between different clock domains to prevent invalid transient states from being captured, ensuring that any sampled value is either the old or new correct multi-bit value.
How can CPU power consumption be reduced in low-power designs using Gray code addressing?
Answer: By significantly reducing the number of state changes of the address bits.
Explanation: In low-power CPU designs, Gray code addressing for instruction memory access patterns significantly reduces the number of state changes of the address bits, leading to lower CPU power consumption.
How do STGCs offer advantages in the fabrication of rotary encoder wheels?
Answer: Their single-track nature reduces manufacturing cost and size.
Explanation: Single-Track Gray Codes (STGCs) offer advantages in rotary encoder fabrication because their single-track nature reduces manufacturing cost and size compared to multi-track binary-reflected Gray codes.
The recursive method for constructing an n-bit Binary-Reflected Gray Code (BRGC) involves prefixing the original (n-1)-bit list with '1' and the reflected list with '0'.
Answer: False
Explanation: The recursive method for constructing an n-bit BRGC involves prefixing the original (n-1)-bit list with '0' and the reflected list with '1', then concatenating them.
The translation of a binary value 'n' to its Gray code equivalent is achieved by computing 'n AND (n << 1)'.
Answer: False
Explanation: Translating a binary value 'n' to Gray code is done by computing 'n XOR (n >> 1)', not 'n AND (n << 1)'.
Gray isometry establishes a correspondence between 'good' linear codes in Z_2^2 and non-linear codes from Z_4.
Answer: False
Explanation: Gray isometry establishes a correspondence between various 'good' codes that are *not necessarily linear* (known as Gray-map images in Z_2^2) and *ring-linear* codes from Z_4.
The Hamming weights of a code are solely significant within coding theory and bear no physical implications.
Answer: False
Explanation: The Hamming weights of a code are significant beyond coding theory for physical reasons, influencing aspects like power consumption or acoustic noise, depending on the application.
What is the bitwise operation used to translate a binary value 'n' into its corresponding Gray code?
Answer: n XOR (n >> 1)
Explanation: A binary value 'n' can be translated into its corresponding Gray code by computing 'n XOR (n >> 1)'.
What mathematical correspondence does Gray isometry establish?
Answer: An isometry between Z_2^2 (Hamming distance) and Z_4 (Lee distance).
Explanation: Gray isometry establishes a bijective mapping that is an isometry between the metric space over the finite field Z_2^2, using the Hamming distance, and the metric space over the finite ring Z_4, using the Lee distance.
What is the significance of Hamming weights beyond coding theory?
Answer: They can influence physical aspects like power consumption or acoustic noise.
Explanation: The Hamming weights of a code are significant beyond coding theory because they can influence physical aspects such as power consumption or acoustic noise, depending on the application.