## --- Day 3: Binary Diagnostic ---

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.)