What happens when you convert counting numbers to binary and then flip or reverse the digits? You write programs on a graphing calculator to generate two new sequences from the natural numbers. The first sequence inverts every binary digit. Zeros become ones and ones become zeros. The result matches what you get from a subtraction rule in computer math. The second sequence reverses the order of binary digits before converting back to decimal. This one reveals surprising patterns. Some are obvious and some are hidden. You derive formulas to explain the patterns for both sequences across at least 1,000 terms.