PLEASE HELP!!! Translate the following into binary and then into grey code
2F16 *
*The number 16 is small and below the letter F
Binary = 10111100010110
Grey Code = 11100010011101
That's what I got.
To translate the number 2F16 into binary, we can follow these steps:
1. Convert each hexadecimal digit to its corresponding 4-bit binary representation:
- 2 (hex) = 0010 (binary)
- F (hex) = 1111 (binary)
2. Concatenate the binary representations to obtain the binary equivalent of 2F16:
- 2F16 (hex) = 001011112 (binary)
Now, to convert the binary representation into gray code:
1. Start with the most significant bit (MSB) as the first bit in the Gray code.
2. The subsequent bits are obtained by performing an XOR operation (exclusive OR) between the current bit and the previous bit.
- The first bit remains the same.
- For the second bit, perform XOR between the first bit and the second bit of the binary representation.
- For the remaining bits, perform XOR between the corresponding bit of the binary representation and the previous bit.
Let's apply the Gray code conversion to the binary representation:
- 0 (binary) remains as is.
- For each subsequent bit, perform XOR between the previous bit and the corresponding bit of the binary representation:
- 0 0 1 0 1 1 1 1 (binary)
Therefore, 2F16 in Gray code is 00101111.
Please note that the number 16 mentioned is not part of the hexadecimal representation, but rather a clarification about its magnitude compared to the letter F.