Each of a set of IID symbols is generated with nonuniform probability by a certain process and is represented by a variable length code according to the following table.Symbol Probability Code wordA 0.53 0B 0.07 111C 0.24 100D 0.06 1100E 0.04 1101F 0.06 101What is the average number of bits per symbol generated? (Give your answer to 3 significant figures, WITHOUT units)
Question
Each of a set of IID symbols is generated with nonuniform probability by a certain process and is represented by a variable length code according to the following table.Symbol Probability Code wordA 0.53 0B 0.07 111C 0.24 100D 0.06 1100E 0.04 1101F 0.06 101What is the average number of bits per symbol generated? (Give your answer to 3 significant figures, WITHOUT units)
Solution
To calculate the average number of bits per symbol generated, we need to multiply the probability of each symbol by the length of its code word and then sum up these products.
Here's how to do it:
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For symbol A, the probability is 0.53 and the code word is 0, which has a length of 1 bit. So, the product is 0.53 * 1 = 0.53.
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For symbol B, the probability is 0.07 and the code word is 111, which has a length of 3 bits. So, the product is 0.07 * 3 = 0.21.
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For symbol C, the probability is 0.24 and the code word is 100, which has a length of 3 bits. So, the product is 0.24 * 3 = 0.72.
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For symbol D, the probability is 0.06 and the code word is 1100, which has a length of 4 bits. So, the product is 0.06 * 4 = 0.24.
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For symbol E, the probability is 0.04 and the code word is 1101, which has a length of 4 bits. So, the product is 0.04 * 4 = 0.16.
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For symbol F, the probability is 0.06 and the code word is 101, which has a length of 3 bits. So, the product is 0.06 * 3 = 0.18.
Now, add up all these products: 0.53 + 0.21 + 0.72 + 0.24 + 0.16 + 0.18 = 2.04.
So, the average number of bits per symbol generated is 2.04.
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