# Day 3: Binary Diagnostic [https://adventofcode.com/2021/day/3](https://adventofcode.com/2021/day/3) ## Description ### Part One The submarine has been making some odd creaking noises, so you ask it to produce a diagnostic report just in case. The diagnostic report (your puzzle input) consists of a list of binary numbers which, when decoded properly, can tell you many useful things about the conditions of the submarine. The first parameter to check is the _power consumption_. You need to use the binary numbers in the diagnostic report to generate two new binary numbers (called the _gamma rate_ and the _epsilon rate_). The power consumption can then be found by multiplying the gamma rate by the epsilon rate. Each bit in the gamma rate can be determined by finding the _most common bit in the corresponding position_ of all numbers in the diagnostic report. For example, given the following diagnostic report: 00100 11110 10110 10111 10101 01111 00111 11100 10000 11001 00010 01010 Considering only the first bit of each number, there are five `0` bits and seven `1` bits. Since the most common bit is `1`, the first bit of the gamma rate is `1`. The most common second bit of the numbers in the diagnostic report is `0`, so the second bit of the gamma rate is `0`. The most common value of the third, fourth, and fifth bits are `1`, `1`, and `0`, respectively, and so the final three bits of the gamma rate are `110`. So, the gamma rate is the binary number `10110`, or _`22`_ in decimal. The epsilon rate is calculated in a similar way; rather than use the most common bit, the least common bit from each position is used. So, the epsilon rate is `01001`, or _`9`_ in decimal. Multiplying the gamma rate (`22`) by the epsilon rate (`9`) produces the power consumption, _`198`_. Use the binary numbers in your diagnostic report to calculate the gamma rate and epsilon rate, then multiply them together. _What is the power consumption of the submarine?_ (Be sure to represent your answer in decimal, not binary.) ### Part Two Next, you should verify the _life support rating_, which can be determined by multiplying the _oxygen generator rating_ by the _CO2 scrubber rating_. Both the oxygen generator rating and the CO2 scrubber rating are values that can be found in your diagnostic report - finding them is the tricky part. Both values are located using a similar process that involves filtering out values until only one remains. Before searching for either rating value, start with the full list of binary numbers from your diagnostic report and _consider just the first bit_ of those numbers. Then: * Keep only numbers selected by the _bit criteria_ for the type of rating value for which you are searching. Discard numbers which do not match the bit criteria. * If you only have one number left, stop; this is the rating value for which you are searching. * Otherwise, repeat the process, considering the next bit to the right. The _bit criteria_ depends on which type of rating value you want to find: * To find _oxygen generator rating_, determine the _most common_ value (`0` or `1`) in the current bit position, and keep only numbers with that bit in that position. If `0` and `1` are equally common, keep values with a _`1`_ in the position being considered. * To find _CO2 scrubber rating_, determine the _least common_ value (`0` or `1`) in the current bit position, and keep only numbers with that bit in that position. If `0` and `1` are equally common, keep values with a _`0`_ in the position being considered. For example, to determine the _oxygen generator rating_ value using the same example diagnostic report from above: * Start with all 12 numbers and consider only the first bit of each number. There are more `1` bits (7) than `0` bits (5), so keep only the 7 numbers with a `1` in the first position: `11110`, `10110`, `10111`, `10101`, `11100`, `10000`, and `11001`. * Then, consider the second bit of the 7 remaining numbers: there are more `0` bits (4) than `1` bits (3), so keep only the 4 numbers with a `0` in the second position: `10110`, `10111`, `10101`, and `10000`. * In the third position, three of the four numbers have a `1`, so keep those three: `10110`, `10111`, and `10101`. * In the fourth position, two of the three numbers have a `1`, so keep those two: `10110` and `10111`. * In the fifth position, there are an equal number of `0` bits and `1` bits (one each). So, to find the _oxygen generator rating_, keep the number with a `1` in that position: `10111`. * As there is only one number left, stop; the _oxygen generator rating_ is `10111`, or _`23`_ in decimal. Then, to determine the _CO2 scrubber rating_ value from the same example above: * Start again with all 12 numbers and consider only the first bit of each number. There are fewer `0` bits (5) than `1` bits (7), so keep only the 5 numbers with a `0` in the first position: `00100`, `01111`, `00111`, `00010`, and `01010`. * Then, consider the second bit of the 5 remaining numbers: there are fewer `1` bits (2) than `0` bits (3), so keep only the 2 numbers with a `1` in the second position: `01111` and `01010`. * In the third position, there are an equal number of `0` bits and `1` bits (one each). So, to find the _CO2 scrubber rating_, keep the number with a `0` in that position: `01010`. * As there is only one number left, stop; the _CO2 scrubber rating_ is `01010`, or _`10`_ in decimal. Finally, to find the life support rating, multiply the oxygen generator rating (`23`) by the CO2 scrubber rating (`10`) to get _`230`_. Use the binary numbers in your diagnostic report to calculate the oxygen generator rating and CO2 scrubber rating, then multiply them together. _What is the life support rating of the submarine?_ (Be sure to represent your answer in decimal, not binary.)