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1. A character in a ASCII system has size 1 byte or 8 bit (1 or 0)
A). How many bit patterns are formed?
B). How many bit patterns have 3 bits 1?
C). How many bit patterns have an even number of bits 1?
Expert Answer
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 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).
hence there are 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
= 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.
