Question & Answer: 1. A character in a ASCII system has size 1 byte or 8 bit (1 or 0) A). How many bit patterns are formed?…..

1. A character in a ASCII system has size 1 byte or 8 bit (1 or 0)

A). How many bit patterns are formed?

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Question & Answer: 1. A character in a ASCII system has size 1 byte or 8 bit (1 or 0) A). How many bit patterns are formed?…..
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B). How many bit patterns have 3 bits 1?

C). How many bit patterns have an even number of bits 1?

Expert Answer

 Solution :

A) Number of bit patterns that can be formed : 28 bit patterns can be formed using 8 bits.

With n bits, 2n bit patterns are possible. So with 8 bits 28 bit patterns possible.

B) Number of bit patterns that have 3 bits 1 :

out of 8 bits , any 3 bits are selected to be 1 and other bits has to be 0.

There are binom{8}{3} ways to select 3 bits out of 8 bits. (we are selecting 3 bits to be 1 out of 8 bits. Which means rest 5 bits are 0 and we choose 3 bits to be 1).

left [ binom{n}{r} =frac{n!}{left ( n-r right )! *r!} right ]

hence there are binom{8}{3} bit patterns possible which has exactly 3 bits 1.

C) Bit patterns with even number of bits 1 :

even number of bits 1 = 0 number of bits 1 + 2 number of bits 1 + 4 number of bits 1 + 8 number of bits 1

=binom{8}{0} +binom{8}{2} +binom{8}{4}+binom{8}{8}

= 1+ 28 + 70 + 1

= 100

hence there are 100 bit patterns that have an even number of bits 1.

if you have any doubts, you can ask in comment section.

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