GATE | GATE IT 2006 | Question 65

In the 4B/5B encoding scheme, every 4 bits of data are encoded in a 5-bit codeword. It is required that the codewords have at most 1 leading and at most 1 trailing zero. How many such codewords are possible?

(A) 14
(B) 16
(C) 18
(D) 20


Answer: (C)

Explanation: The possible codewords should not have 00xxx or xxx00
=> Total possible combinations of 5 bits – for (00xxx or xxx00)+ (00×00) {as 00×00 is subtracted twice once each from both cases}
=> 232 – (8+8) +2 = 18

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