For $R=\frac{4}{7},$ the four source bits are denoted by $x_0,x_1,x_2,x_3$ then the extra or redundant or the parity$-$check bits are represented by $x_4,x_5,x_6.$

i$.$ Using MOD$-2$ arithmetic, Show how $x_4,x_5,x_6$ are determined?

Mks $3$

ii$.$ At the receiver side, show how it estimate the four transmitted bits from the Mks $3$ garbled seven bit codes

iii. Outline the decoding algorithm for the $(7,4)$ Hamming Code given the received Mks $4$ vector $y.$