Question

The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.
For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:
00 - 0
01 - 1
11 - 3
10 - 2

Answer 1

Gray code is used in computing and digital communications for error correction, generating sequences where each number differs by one bit. Given n bits, it starts with 0 and flips one bit to generate the next number. Examples include transmitting cell phone conversations and television images as digital data.

Step-by-step explanation:

The Gray code is a binary numeral sequence often used in computing and digital communications, where two subsequent numbers differ by only one bit. The process of generating a Gray code sequence starts with 0 and involves flipping one bit at a time to generate the next number in the sequence. This property is beneficial for error correction in digital data transmission due to the minimal change from one value to the next.

For example, constructing the Gray code sequence for a 2-bit binary number involves the following steps:

1. Start with an initial sequence of 0 (binary: 00).
2. Flip one bit to get 1 (binary: 01).
3. Flip one bit to get 3 (binary: 11), taking care not to reverse the last change.
4. Flip one bit that hasn't been changed last to get 2 (binary: 10).

The resulting Gray code sequence is [0, 1, 3, 2], which can be visualized as 00, 01, 11, 10 in binary form. When a cell phone conversation or a television voice and video image gets transmitted as digital data, systems often use binary sequences or techniques like Gray codes that minimize errors due to their one-bit difference property.