## 18 Questions

In genetic algorithms, why are Gray codes favored for representing information?

They allow for mostly incremental changes

What is the Gray code equivalent of the decimal number 13?

1011

What is the primary advantage of using Gray codes in computers for program memory addressing?

Minimizing power consumption

How are the next three numbers in the four-bit Gray code sequence after 0101 determined?

By appending '1' to the eight three-bit numbers in reverse order

Which type of codes are used to represent alphanumeric data?

Character codes

What do Gray codes minimize in program memory addressing?

Number of address lines changing state

What is the process to convert a Gray code number into its binary equivalent?

Adding the MSB in the binary number to the MSB in the Gray code number.

Which type of Gray code uses non-Boolean symbols for encoding?

n-ary Gray code

What is the word length for a ternary Gray code (n = 3)?

Two-digit

In a quaternary Gray code (n = 4), what are the independent digits used?

0, 1, 2, 3

What is another term for binary-reflected Gray code?

Binary Gray code

Which step is taken after obtaining the third MSB during the conversion process from a Gray code to its binary equivalent?

Consider a carry from the addition.

What is the value of the decimal equivalent of the excess-3 code 1001 0111 0000.0100 0010?

(970.42)10

Which property of the Gray code ensures that the maximum error is minimized when encoding data?

Consecutive code words differ by only one bit.

What is the binary-reflected Gray code equivalent of the decimal number 7?

0010

Which of the following statements about the Gray code is true?

The last entry in the code rolls over to the first entry.

How can the Gray code pattern for a given number of bits be remembered?

The least significant bit follows a repetitive pattern of '2', the next higher bit follows a pattern of '4', and so on.

What is the maximum number of bits that can differ between two consecutive Gray code words of the same word length?

1

## Study Notes

### Gray Code Conversion

- The third MSB in the binary number is obtained by adding the second MSB in the binary number to the third MSB in the Gray code number, ignoring any carry.
- The conversion process continues until the LSB of the binary number is obtained.

### n-ary Gray Code

- The n-ary Gray code, also known as the non-Boolean Gray code, uses non-Boolean symbols for encoding.
- The generalized representation of the code is the (n, k) Gray code, where n is the number of independent digits used and k is the word length.
- Examples of n-ary Gray codes include ternary Gray code (n = 3) and quaternary Gray code (n = 4).

### Applications of Gray Code

- Gray codes minimize power consumption in computers by reducing the number of address lines changing state.
- Gray codes are useful in genetic algorithms as they allow for mostly incremental changes.

### Binary-Gray Conversion

- The binary equivalent of a decimal number can be converted to Gray code by adding the second MSB in the binary number to the third MSB in the Gray code number.
- Examples of binary-Gray conversion include decimal 13 (binary 1101) to Gray code 1011 and Gray code 1111 to binary 1010.

### Alphanumeric Codes

- Alphanumeric codes, also called character codes, are binary codes used to represent alphanumeric data.
- Examples of alphanumeric codes include subtracting 0011 from each four-bit group to obtain a new number.

### History of Gray Code

- The Gray code was designed by Frank Gray at Bell Labs and patented in 1953.
- The Gray code is an unweighted binary code in which two successive values differ only by 1 bit.

### Properties of Gray Code

- The Gray code has the cyclic property, where the last and first entries differ by only 1 bit.
- The Gray code can be remembered by patterns of repetitive bits, such as the least significant bit following a pattern of ‘2’ and the next higher adjacent bit following a pattern of ‘4’.

Explore how Gray codes are used to minimize power consumption in program memory addressing in computers. Discover the importance of Gray codes in genetic algorithms for incremental changes and occasional big leaps. Test your knowledge with questions on finding Gray code equivalents and binary conversions.

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