Understanding Codes with Single Bit Changes

The question asks about a specific type of code where the representation of successive numbers differs by only one bit. This property is important in various applications, especially in digital systems and sensors, because it minimizes errors that might occur during transitions between numbers.

Analyzing the Options

Let's look at the provided options:

1. Hamming code: Hamming codes are primarily used for error detection and correction in data transmission or storage. They add redundant bits to the original data to identify and fix single-bit errors. They do not have the property of successive numbers differing by only one bit in their encoding scheme for numerical sequences.
2. BCD (Binary-Coded Decimal) code: BCD represents each decimal digit (0-9) using a 4-bit binary code. For example, the decimal number 12 is represented as 0001 0010 in BCD. Successive numbers in BCD do not necessarily differ by only one bit. For example, the transition from decimal 4 (0100) to 5 (0101) involves a one-bit change. However, the transition from 9 (1001) to 10 (0001 0000) involves multiple bit changes across two 4-bit groups.
3. GRAY code: Gray code, also known as Reflected Binary Code, is a binary numeral system where two successive values differ in only one bit. This characteristic is specifically designed into the code.
4. ASCII code: ASCII (American Standard Code for Information Interchange) is a character encoding standard used to represent text in computers and other devices. It assigns unique numerical values to letters, numbers, symbols, and control characters. It is not used to represent numerical sequences in a way that successive numbers have a one-bit difference property.

Why Gray Code Fits the Description

The key property mentioned in the question is "only one bit changes between successive numbers". This is the defining characteristic of the Gray code. Let's compare standard binary representation with Gray code for a few numbers to see this difference:

Observe the transitions in the table:

• Binary 0 (0000) to 1 (0001): One bit change (the rightmost bit). Gray 0 (0000) to 1 (0001): One bit change.
• Binary 1 (0001) to 2 (0010): Two bit changes (second and fourth bits from right). Gray 1 (0001) to 2 (0011): One bit change (the third bit from right).
• Binary 2 (0010) to 3 (0011): One bit change (the rightmost bit). Gray 2 (0011) to 3 (0010): One bit change (the rightmost bit).
• Binary 3 (0011) to 4 (0100): Three bit changes. Gray 3 (0010) to 4 (0110): One bit change (the second bit from left).

As the table shows, the Gray code consistently has only one bit change between successive numbers, while the binary code does not. This unique property makes Gray code suitable for applications like rotary encoders and Karnaugh maps, where single-bit changes are advantageous to avoid errors during transitions.

Conclusion

Based on the definition and the property described in the question, the code where only one bit changes between successive numbers is the Gray code.

Revision Table: Digital Codes Overview

Additional Information on Gray Code Applications

Gray code's unique property makes it valuable in specific areas of digital design and systems:

• Rotary Encoders: Gray code is widely used in positional sensors like rotary encoders. As the encoder rotates, it generates a digital code representing the angle. Using Gray code ensures that as the encoder moves from one position to the next, only one bit changes. This prevents potential errors (transient incorrect readings) that could occur with binary code if multiple bits change simultaneously but at slightly different speeds.
• Karnaugh Maps (K-maps): In digital circuit design, K-maps are used for simplifying Boolean expressions. The grid of a K-map is labeled using Gray code to ensure that adjacent cells (representing minterms or maxterms) differ by only one variable. This property is essential for grouping terms effectively to find simplified expressions.
• Error Prevention: The single-bit change property helps prevent 'glitches' or transient false outputs in digital systems when transitioning between states represented by successive numbers.