Convert 1010 to 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 is useful in digital systems to prevent spurious output from switches and to improve error correction in digital communications such as digital terrestrial television and some cable TV systems.

To convert a binary number to Gray code, follow these steps:

1. Write down the binary number.
2. The most significant bit (MSB) of the Gray code is the same as the MSB of the binary number.
3. For each next bit of the Gray code, perform an exclusive OR (XOR) operation between the current bit and the previous bit of the binary number.

Let's convert the binary number 1010 to Gray code using the steps mentioned above:

Step	Operation	Binary Number	Gray Code
1	-	1010	-
2	-	1	1
3	1 XOR 0	0	1
3	0 XOR 1	1	11
3	1 XOR 0	0	111

The XOR operation can be represented by the following truth table:

A (Binary)	B (Previous Bit)	A XOR B (Result)
0	0	0
0	1	1
1	0	1
1	1	0

Now, let's apply the XOR operation to each bit:

• The MSB of the binary number is 1, so the MSB of the Gray code is also 1.
• The second bit of the binary number is 0. We XOR it with the first bit (1): 1 XOR 0 = 1.
• The third bit of the binary number is 1. We XOR it with the second bit (0): 0 XOR 1 = 1.
• The fourth bit of the binary number is 0. We XOR it with the third bit (1): 1 XOR 0 = 1.

Therefore, the binary number 1010 in Gray code is 1111.