a bit is either 0 or 1,a byte is a sequence of 8 bits find,

(a) the number of bytes that can be formed

(b) the number of bytes that begin with 11 and ends with 11

(c) the number of bytes that begin with 11 and do not end with 11

(d) the number of bytes that begin with 11or end with11

Dear Student!!

1 byte is a sequence of 8 bits.

(a) Number of bytes that can be formed : 

For every 1 position we have 2 options 0 or 1.

Number of such positions = 8

∴ Number of bytes that can be formed = 2⁸ = 256

(b) 

The 4 vacant positions can be filled in 2⁴ = 16 ways

Thus, number of bytes that begin with 11 and end with 11 is 16.

(c)

Number of bytes that begin with 11 = 2⁶ = 64

Required number of bytes = 64 – number of bytes that begin with 11 and end with 11

 = 64 – 16  (found out in (b))

 = 48

(d) (found in (c)) Number of bytes begin with 11 = 64

Similarly, number of bytes that end with 11 = 64

Adding the above two = 64 + 64 = 128

Each bytes that begins and ends with 11 is counted twice.

So, we need to subtract it.

Thus, required answer = 128 – 16  (using (b))

 = 112

Cheers..!!