To encode the 16-bit data with Hamming error code, we need to add three parity bits at positions 1, 2, and 4. The data bits will occupy the remaining positions: 3, 5, 6, 7, 9, 10, 11, and 12.
The parity bits will be calculated by XORing specific groups of data bits. The bit positions used to calculate each parity bit will be those with a "1" in the corresponding position when the bit number is written in binary.
Using this method, we can calculate the parity bits as follows:
Parity bit 1 (position 1): XOR of data bits 3, 5, 6, 7, 11, and 12.