Apply Huffman - Coding procedure for M-2.And find the coding efficiency.Given: [X]= [xl x2 x3 x4 x5 x6 x7 x8][P}-[0.1,0.25,0.15,0.05,0.15,0.1,0.05,0.15]

To apply the Huffman coding procedure for M-2, we need to follow these steps:

Step 1: Arrange the symbols in decreasing order of their probabilities. Given: [X] = [x1 x2 x3 x4 x5 x6 x7 x8] [P] = [0.1, 0.25, 0.15, 0.05, 0.15, 0.1, 0.05, 0.15]

Arranging the symbols in decreasing order of their probabilities: [x2 x3 x5 x8 x6 x1 x4 x7] [0.25, 0.15, 0.15, 0.15, 0.1, 0.1, 0.05, 0.05]

Step 2: Combine the two symbols with the lowest probabilities and create a new symbol with the sum of their probabilities. [x2 x3 x5 x8 x6 x1 x4 x7] [0.25, 0.15, 0.15, 0.15, 0.1, 0.1, 0.05, 0.05]

Combine x7 and x4: [x2 x3 x5 x8 x6 x1 (x4x7)] [0.25, 0.15, 0.15, 0.15, 0.1, 0.1, 0.1]

Combine x6 and (x4x7): [x2 x3 x5 x8 (x6x4x7) x1] [0.25, 0.15, 0.15, 0.15, 0.2, 0.1]

Combine x1 and x5: [x2 x3 (x1x5) x8 (x6x4x7)] [0.25, 0.15, 0.25, 0.15, 0.2]

Combine x3 and (x1x5): [x2 (x3x1x5) x8 (x6x4x7)] [0.25, 0.4, 0.15, 0.2]

Combine x8 and (x6x4x7): [x2 (x3x1x5) (x8x6x4x7)] [0.25, 0.4, 0.35]

Combine (x3x1x5) and (x8x6x4x7): [(x2x3x1x5) (x8x6x4x7)] [0.65, 0.35]

Step 3: Repeat steps 2 until only two symbols remain.

Step 4: Assign 0 and 1 to the branches of the binary tree, with 0 representing the left branch and 1 representing the right branch.

Step 5: Assign the binary code to each symbol by traversing the binary tree from the root to the symbol.

The coding efficiency can be calculated by multiplying the probability of each symbol by the length of its corresponding binary code and summing them up.