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## Main Question or Discussion Point

Suppose that A is an n-digit binary string: [itex] a_{0}a_{1}a_{2}...a_{n} [/itex] where [itex]a_{i}[/itex] is a member of the set [itex]\{0,1\}[/itex]

Now define the following sequence of operations:

1) Complement each digit in A to get a binary string A'

2) A'' = A' + 1 (here + is taken to mean binary addition rather than the boolean OR)

3) Complement each digit in A'' to get a new binary string A'''

4) A'''' = A''' + 1 (here + is taken to mean binary addition rather than the boolean OR)

Prove that for all A, A'''' = A

I appreciate all the help.

BiP

Now define the following sequence of operations:

1) Complement each digit in A to get a binary string A'

2) A'' = A' + 1 (here + is taken to mean binary addition rather than the boolean OR)

3) Complement each digit in A'' to get a new binary string A'''

4) A'''' = A''' + 1 (here + is taken to mean binary addition rather than the boolean OR)

Prove that for all A, A'''' = A

I appreciate all the help.

BiP