Zeroes and Ones - 30 points

Writeup by poortho

Problem Statement: Bit String Flicking

How many solutions are there for X in the expression:

LCIRC -3 (01011 AND X OR 10100) = 01101

Hint:

Try simplifying it?

Writeup

This problem is a simple bit string flicking equation. Let's begin.

First, LCIRC-3 means that you cycle the bits left 3 times. The inverse of LCIRC-3 is RCIRC-3, so we can rewrite the equation as 01011 AND X OR 10100 = 10101

Then, order of operations dictates that we perform the AND then the OR.

Thus, because the OR is applied last, we know that the 2nd and 4th bit of 01011 AND X has to be 0, the 5th bit has to be 1, and the 1st and 3rd bit can be anything.

So now we have 01011 AND X = ?0?01. Again, we see that the 1st and 3rd bit of X can be anything. We also see that the 5th bit has to be 1, and the 2nd and 4th bit must be 0.

Thus, our answer is 2^(number of ?'s) = 2^2 = 4, which is our flag.

Flag

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