The Function fbinary strings binary strings In each case fi

The Function f:{binary strings} --> {binary strings}. In each case, find f(s).

a) s = {000, 1011, 10001}, f(x) = the second bit in x

b) s = {111, 100, 0111}, f(x) = the binary string that is the sum of the first and last bit

c) s = {001, 11, 101}, f(x) = the binary string that is equal to x + 1

Solution

Given The Function f:{binary strings} --> {binary strings}.

a) s = {000, 1011, 10001}, f(x) = the second bit in x.

f(s) should have strings such as the second bit of strings of s.

Therefore, f(s) = {0, 0, 0}

b) s = {111, 100, 0111}, f(x) = the binary string that is the sum of the first and last bit

f(s) should have strings such as the sum of the first and last bit of s.

111: sum of first bit and last bit =1+1 =10 (carry 1 and sum 0)

100: sum of first bit and last bit =1+0 =1

0111: sum of first bit and last bit =0+1 =1

Therefore, f(s) = {10, 1, 1}

c) s = {001, 11, 101}, f(x) = the binary string that is equal to x + 1

  f(s) should have strings such as the binary string that is equal to x + 1

001+1 = 010

11+1 = 100

101+1 = 110

Therefore, f(s) = {010, 100, 110}