Solution

The Correct answer is Option 2

Key Points

Gray code equivalent to decimal number 8 is:

• Gray code is a binary numeral system where two successive values differ in only one bit.
• The decimal number 8 in binary is represented as 1000. To convert it into Gray code:
• The most significant bit (MSB) of the Gray code is the same as the binary representation MSB. So, the MSB remains 1.
• For the subsequent bits, each bit of the Gray code is obtained by XORing the corresponding binary bit with the bit before it. Following this method for 8 (1000 in binary), we get:
• • MSB = 1
  • Second bit = 1 XOR 0 = 1
  • Third bit = 0 XOR 0 = 0
  • Fourth bit = 0 XOR 0 = 0
• Thus, the Gray code for 8 becomes 1100.

Option 1: 1000:

• This is the binary representation of the decimal number 8, not its Gray code equivalent.
• Gray code differs from binary representation in that two successive values differ by only one bit.

Option 2: 1100:

• This is the correct Gray code equivalent of the decimal number 8.
• Following the conversion steps described above, the decimal number 8 (1000 in binary) converts to 1100 in Gray code.

Option 3: 1010:

• This is not the correct Gray code for 8.
• It does not follow the rule of successive bits differing by only one bit, which is a requirement for Gray code.

Option 4: 1110:

• This is also incorrect.
• While it starts with the correct MSB (1), the subsequent bits do not match the XOR operation required for Gray code conversion.