Prove by induction that the number of different binary strin

Prove by induction that the number of different binary strings with n bits is 2^n

Solution

different binary strings for 1 bits:2^1=2 {0 or 1}

different binary strings for 2 bits:2^2=4 {00,01,10,11}

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different binary strings for k bits:2^k it is true

different binary strings for k+1 bits:2^(k+1) it for k+1 proved

so that   this is for n also proved.