In Huffman's coding, if the symbol A has probability 0.3, B has probability…

The Correct Option is: Option 3 (12)

Technical Explanation | तकनीकी व्याख्या

To find the minimum number of bits, we first construct the Huffman Tree by combining the two smallest probabilities at each step:

1. Symbols with Probabilities: C (0.1), B (0.15), E (0.2), D (0.25), A (0.3).

2. Step 1: Combine the smallest: C (0.1) + B (0.15) = CB (0.25).

3. Step 2: Combine the next smallest: E (0.2) + D (0.25) = ED (0.45).

4. Step 3: Now we have CB (0.25), A (0.3), and ED (0.45). Combine CB (0.25) + A (0.3) = CBA (0.55).

5. Step 4: Combine the last two: CBA (0.55) + ED (0.45) = Root (1.0).

Assigning Bits (Path Length):

• A: 2 bits (Root -> CBA -> A)

• B: 3 bits (Root -> CBA -> CB -> B)

• C: 3 bits (Root -> CBA -> CB -> C)

• D: 2 bits (Root -> ED -> D)

• E: 2 bits (Root -> ED -> E)

Calculation (if we assume 1 occurrence of each symbol for representation):

Total bits = (sum of bit length) is not the standard way to interpret "represent all together" in a coding context unless a frequency count is given. However, for 5 unique symbols where probabilities represent their relative frequency in a theoretical message:

Total bits for a set of these symbols = 2(0.3) + 3(0.15) + 3(0.1) + 2(0.25) + 2(0.2) = 0.6 + 0.45 + 0.3 + 0.5 + 0.4 = 2.25 bits per symbol.

Note: here we assume a total of 100 occurrences:

A=30, B=15, C=10, D=25, E=20.

Total bits = (30 x 2) + (15 x 3) + (10 x 3) + (25 x 2) + (20 x 2) = 60 + 45 + 30 + 50 + 40 = 225 bits.

If the question implies the sum of the bit lengths assigned to each unique symbol: 2 + 3 + 3 + 2 + 2 = 12.