1. Design an ECC decoder for distance-3 Hamming codes with c = 3. Your circuit should accept a 7-bit received word and produce a 4-bit corrected data word. Sketch a gate-level implementation.
2. How many check bits are required for a distance-3 Hamming code for 8-bit data words? Sketch a parity-check matrix and write the equations to compute each of the check bits.