Which of the following codes is also known as reflected binary code?

Question

Prepp Team · Accepted Answer

Understanding Reflected Binary Code: Gray Code Explained

The question asks to identify the code that is also known as reflected binary code. Let's analyze the options provided to understand which one fits this description.

What is Reflected Binary Code?

Reflected binary code is a type of binary numeral system where two successive values differ in only one bit. This unique property makes it valuable in certain applications.

The term "reflected" comes from the way the code can be constructed. For example, a 3-bit Gray code can be generated from a 2-bit Gray code by reflecting the 2-bit code and adding a prefix bit.

Analyzing the Options

Excess-3 code: This is a self-complementing BCD (Binary Coded Decimal) code. Each decimal digit is represented by its 4-bit binary equivalent plus 3. Successive values typically change in more than one bit. Thus, it is not a reflected binary code.
Gray code: Gray code, also known as Reflected Binary Code (RBC) or simply reflected binary, is specifically designed so that adjacent code words differ by only one bit. This aligns perfectly with the definition of reflected binary code.
Straight binary code: This is the standard binary representation where each position represents a power of 2. Successive values can differ by multiple bits (e.g., 001 (1) to 010 (2) differs by two bits). It is not a reflected binary code.
Error code: This is a general term referring to codes designed to detect or correct errors during data transmission or storage (e.g., parity codes, Hamming codes). While some error detection/correction techniques might use binary representation, "Error code" is not a specific type of reflected binary code.

Why Gray Code is Reflected Binary Code

Gray code is constructed such that transitions between consecutive numbers involve only a single bit change. This is crucial in systems where mechanical or electrical errors can occur during transitions, as a single bit change minimizes the possibility of reading an incorrect intermediate value.

Here is a comparison of 3-bit straight binary code and 3-bit Gray code:

Decimal	Straight Binary	Gray Code (Reflected Binary)
0	000	000
1	001	001
2	010	011
3	011	010
4	100	110
5	101	111
6	110	101
7	111	100

As you can observe in the table, each step in the Gray code sequence involves only one bit flip compared to the straight binary code where multiple bits can change (e.g., from 3 (011) to 4 (100)). This property is the defining characteristic of reflected binary code.

Based on the analysis, Gray code is indeed known as reflected binary code.

Revision Table: Key Code Types

Code Name	Description	Property Related to Bit Change
Straight Binary Code	Standard binary representation	Multiple bits can change between successive numbers
Gray Code (Reflected Binary)	Non-weighted code	Only one bit changes between successive numbers
Excess-3 Code	Weighted BCD + 3	Multiple bits can change between successive numbers
Error Codes	Codes for detection/correction	Varies depending on the specific code

Additional Information: Applications of Gray Code

The single-bit change property of Gray code makes it useful in various applications, including:

Shaft Encoders: Devices that measure rotational position or speed often use Gray code to avoid reading ambiguous intermediate values when transitioning between positions.
Karnaugh Maps (K-maps): K-maps use Gray code ordering for rows and columns to ensure that adjacent cells represent minterms that differ by only one variable, simplifying the identification of product terms.
Preventing Glitches: In asynchronous digital systems, using Gray code for counters or state encoding can help prevent race conditions and glitches caused by multiple bits changing simultaneously.