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Questions and Answers
What is the purpose of adding a parity bit to a code word?
What is the purpose of adding a parity bit to a code word?
- To increase the number of ones in the data
- To determine odd or even parity (correct)
- To decrease the number of ones in the data
- To detect errors in the data
In the ASCII encoding scheme, how is the letter 'S' represented with odd parity?
In the ASCII encoding scheme, how is the letter 'S' represented with odd parity?
- (11010011) (correct)
- (11110011)
- (1010011)
- (1000011)
What can be inferred if a data word with even parity has an odd number of ones?
What can be inferred if a data word with even parity has an odd number of ones?
- The data word has even parity
- An error has occurred (correct)
- There are no errors in the data
- The data word is correct
What limitation does the parity bit scheme have in detecting errors?
What limitation does the parity bit scheme have in detecting errors?
How does the repetition code handle error detection?
How does the repetition code handle error detection?
What makes the repetition code self-correcting for single-bit errors?
What makes the repetition code self-correcting for single-bit errors?
What is the output of a NAND gate if all inputs are 1?
What is the output of a NAND gate if all inputs are 1?
How is the output behavior of a NOR gate related to the inputs?
How is the output behavior of a NOR gate related to the inputs?
What is the Boolean expression for the output of an XOR gate?
What is the Boolean expression for the output of an XOR gate?
When does a NAND gate output 1?
When does a NAND gate output 1?
What is the truth table for a two-input NOR gate like?
What is the truth table for a two-input NOR gate like?
Why can't the output behavior of an XOR gate be extended to gates with 3 or more inputs?
Why can't the output behavior of an XOR gate be extended to gates with 3 or more inputs?
What is the purpose of arranging cells in a Karnaugh map using Gray code ordering?
What is the purpose of arranging cells in a Karnaugh map using Gray code ordering?
Why is it mentioned that the input bit change between two neighboring 1s in the Karnaugh map has no effect on the output?
Why is it mentioned that the input bit change between two neighboring 1s in the Karnaugh map has no effect on the output?
How does the number of cells in a Karnaugh map for four variables compare to the number of rows in a truth table for the same variables?
How does the number of cells in a Karnaugh map for four variables compare to the number of rows in a truth table for the same variables?
What do 40 1s placed in cells representing minterms in SoP indicate in a Karnaugh map?
What do 40 1s placed in cells representing minterms in SoP indicate in a Karnaugh map?
How does a Karnaugh map simplify expressions compared to a truth table approach?
How does a Karnaugh map simplify expressions compared to a truth table approach?
What characteristic ensures that physically adjacent cells in a Karnaugh map are logical neighbors as well?
What characteristic ensures that physically adjacent cells in a Karnaugh map are logical neighbors as well?
How many bits are required to code 36 alphanumeric elements of information?
How many bits are required to code 36 alphanumeric elements of information?
What is the term used to represent the binary equivalent of each decimal digit in BCD?
What is the term used to represent the binary equivalent of each decimal digit in BCD?
How many combinations out of 16 are utilized to represent decimal digits in BCD?
How many combinations out of 16 are utilized to represent decimal digits in BCD?
What is the popular example of a unit distance code where adjacent codes differ only in one bit?
What is the popular example of a unit distance code where adjacent codes differ only in one bit?
Where are Gray codes commonly used?
Where are Gray codes commonly used?
When does an expanded code become necessary according to the text?
When does an expanded code become necessary according to the text?
When do flip-flops change states?
When do flip-flops change states?
Which term describes inputs like clear (CLR) and preset (PRE) that are active when the input signal is low?
Which term describes inputs like clear (CLR) and preset (PRE) that are active when the input signal is low?
What does the bubble in the symbol for clear and preset signals indicate?
What does the bubble in the symbol for clear and preset signals indicate?
In an S-R flip-flop, what enables the information from the S or R input to reach the output?
In an S-R flip-flop, what enables the information from the S or R input to reach the output?
What state is reached in an S-R flip-flop with S=1, R=0, and CP=1?
What state is reached in an S-R flip-flop with S=1, R=0, and CP=1?
What happens to the output of gate 3 in an S-R flip-flop when CP input remains at 0?
What happens to the output of gate 3 in an S-R flip-flop when CP input remains at 0?
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Study Notes
Karnaugh Map (K-map)
- A K-map consists of an array of cells, each representing a possible combination of inputs.
- Cells are arranged to that each cell's input combination differs from adjacent cells by only a single bit, called Gray code ordering.
- The number of cells in a K-map is equal to the total number of possible input variable combinations.
- For three variables, the number of cells is 2³ = 8. For four variables, the number of cells is 2⁴ = 16.
Error Detection and Correction
- Parity encoding scheme is a simple one and requires only one extra bit.
- If the system is using even parity and we find an odd number of ones in the received data word, we know that an error has occurred.
- The scheme is meaningful only for single errors. If two bits in a data word were received incorrectly, the parity bit scheme will not detect the faults.
- Repetition Code makes use of repetitive transmission of each data bit in the bit stream.
- In the case of single-bit errors, the correct bit can be taken as the majority bit.
Logic Gates
- NAND gate: output from the NAND gate is 0 if and only if all of the inputs are 1, otherwise the output is 1.
- NOR gate: output from the NOR gate is 1 if and only if all of the inputs are 0, otherwise the output is 0.
- XOR gate: output is similar to that from the OR gate except it is 0 when both inputs are 1. For 3 or more inputs, an XOR gate gives an output value of 1 when there are an odd number of 1's on the inputs to the gate.
Codes
- Binary Coded Decimal (BCD): a representation of decimal numbers in binary form, requiring at least four bits to represent ten decimal digits.
- Unit Distance Codes (Gray Code): codes in which adjacent codes differ only in one bit, used in position sensing transducers like shaft encoders.
- Alphanumeric Codes: expanded codes used when information to be encoded includes entities other than numerical values.
Flip-Flops
- Flip-flops are edge triggered, changing states when the clock goes from 0 to 1 (positive/rising edge) or when the clock goes from 1 to 0 (negative/falling edge).
- Asynchronous Inputs: flip-flops have clear (CLR) and preset (PRE) terminals, which are active when the input signal is low (Active Low Input).
- S-R Flip Flop: a flip-flop circuit constructed from two NAND gates or two NOR gates, with a clock pulse (CP) input.
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