Which of the following is termed as the minimum error code?

Different binary codes are designed for different purposes. A code is called a minimum error code (also known as a unit-distance code) when moving from one value to the very next value changes only a single bit.

Gray code has exactly this property, consecutive numbers in the sequence differ in only one bit position. For example, going from \(3\) to \(4\) in gray code changes just one bit, whereas in ordinary binary several bits can change at once (\(011\) to \(100\)). This single-bit-change property means that if an error occurs while a value is being read or transmitted, such as by a mechanical sensor or rotary encoder, the resulting misread value is at most one step away from the true value, which minimises the size of any error.

Ordinary binary code, excess-3 code, and octal code do not have this single-bit-change guarantee between consecutive values, several bits can flip at once, so a misread can jump far from the intended value.

Exam tip: whenever a question links "minimum error" or "reduces transmission or reading errors" to a binary code, the answer is gray code, because of its one-bit-change property between successive values.