Question

A computer executes four instructions that are designated by the codewords (00,01,10,11). Assuming that the instructions are used independently with probabilities (1/2,1/8,1/8, 1/4 ),

calculate the percentage by which the number of bits used for the instructions may be reduced by the use of an optimum source code. Construct a Huffman code to realize the reduction.

Answer 1

To calculate the percentage by which the number of bits used for the instructions may be reduced by the use of an optimum source code, we can use Huffman coding.

Step-by-step explanation:

To calculate the percentage by which the number of bits used for the instructions may be reduced by the use of an optimum source code, we can use Huffman coding. Huffman coding is a variable-length prefix coding technique that assigns shorter codewords to more frequently occurring symbols.

To construct a Huffman code, we start by creating a table with the instructions and their probabilities. Then, we build a binary tree where each leaf node represents an instruction and its probability. The codeword for each instruction is determined by traversing the binary tree.

Applying Huffman coding to the given probabilities (1/2, 1/8, 1/8, 1/4), we can calculate the average number of bits used for the instructions before and after Huffman coding. The reduction percentage can be calculated as the difference between the average number of bits used before and after, divided by the average number of bits used before, multiplied by 100.