Gray Codes and Program Memory Quiz

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’.