Binary Coded Decimal (BCD) Test: BCD Quiz and Flashcards

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What is the purpose of adding a parity bit to a code word?

To determine odd or even parity

In the ASCII encoding scheme, how is the letter 'S' represented with odd parity?

(11010011)

What can be inferred if a data word with even parity has an odd number of ones?

An error has occurred

What limitation does the parity bit scheme have in detecting errors?

It can only detect single errors Signup and view all the answers

How does the repetition code handle error detection?

By transmitting data bits in groups of three Signup and view all the answers

What makes the repetition code self-correcting for single-bit errors?

Choosing the majority bit as correct Signup and view all the answers

What is the output of a NAND gate if all inputs are 1?

0 Signup and view all the answers

How is the output behavior of a NOR gate related to the inputs?

It is the OR function of inputs Signup and view all the answers

What is the Boolean expression for the output of an XOR gate?

$A \oplus B$ Signup and view all the answers

When does a NAND gate output 1?

If at least one input is 0 Signup and view all the answers

What is the truth table for a two-input NOR gate like?

<table> <thead> <tr> <th>A</th> <th>B</th> <th>Out</th> </tr> </thead> <tbody> <tr> <td>0</td> <td>1</td> <td>0</td> </tr> <tr> <td>1</td> <td>0</td> <td>1</td> </tr> </tbody> </table> Signup and view all the answers

Why can't the output behavior of an XOR gate be extended to gates with 3 or more inputs?

The XOR operation applies to an odd number of inputs only Signup and view all the answers

What is the purpose of arranging cells in a Karnaugh map using Gray code ordering?

To ensure that physical neighbours in the array are logical neighbours as well. Signup and view all the answers

Why is it mentioned that the input bit change between two neighboring 1s in the Karnaugh map has no effect on the output?

To explain the concept of redundancy detection. Signup and view all the answers

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?

The number of cells is always equal to the number of rows. Signup and view all the answers

What do 40 1s placed in cells representing minterms in SoP indicate in a Karnaugh map?

Proper grouping for simplification. Signup and view all the answers

How does a Karnaugh map simplify expressions compared to a truth table approach?

By properly grouping cells based on input combinations. Signup and view all the answers

What characteristic ensures that physically adjacent cells in a Karnaugh map are logical neighbors as well?

Gray code ordering. Signup and view all the answers

How many bits are required to code 36 alphanumeric elements of information?

6 bits Signup and view all the answers

What is the term used to represent the binary equivalent of each decimal digit in BCD?

Binary Coded Decimal Signup and view all the answers

How many combinations out of 16 are utilized to represent decimal digits in BCD?

10 combinations Signup and view all the answers

What is the popular example of a unit distance code where adjacent codes differ only in one bit?

Gray code Signup and view all the answers

Where are Gray codes commonly used?

Shaft encoder Signup and view all the answers

When does an expanded code become necessary according to the text?

When information includes entities other than numerical values Signup and view all the answers

When do flip-flops change states?

When the clock goes from 0 to 1 Signup and view all the answers

Which term describes inputs like clear (CLR) and preset (PRE) that are active when the input signal is low?

Active Low Input Signup and view all the answers

What does the bubble in the symbol for clear and preset signals indicate?

Inverted signal Signup and view all the answers

In an S-R flip-flop, what enables the information from the S or R input to reach the output?

Clock pulse (CP) input Signup and view all the answers

What state is reached in an S-R flip-flop with S=1, R=0, and CP=1?

Set state Signup and view all the answers

What happens to the output of gate 3 in an S-R flip-flop when CP input remains at 0?

Remains at 0 Signup and view all the answers

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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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