diff --git a/src/part1/bin_and_hex.md b/src/part1/bin_and_hex.md index 5ca35880..08c1a7ac 100644 --- a/src/part1/bin_and_hex.md +++ b/src/part1/bin_and_hex.md @@ -133,12 +133,41 @@ Answer the below questions on Binary and Conversions by hand! Reaching these answers can change drastically, this is just one way to solve such problems. ### Answer 1 --- -- The __BASE 10__ number `96` converts to `%0110 0000` in __BASE 2__, This can be found using the _"Short Division by 2 with Remainder"_ method. -- From there you can convert __BASE 2__ `%0110 0000` to __BASE 6__ by using the _"Powers Method"_ resulting in `54432` as our final answer! +- The __BASE 10__ number `96` converts to __BASE 6__ `240`. +- This can be found by repeatedly dividing the number by 6 and keeping track of the remainders: + + ``` + 96 ÷ 6 = 16 remainder 0 + 16 ÷ 6 = 2 remainder 4 + 2 ÷ 6 = 0 remainder 2 + ``` + + Reading from bottom to top gives the final result: `240`. ### Answer 2 --- -- The __BASE 16__ number `$FF` converts to `%1111 1111` in __BASE 2__, You can use the base conversion chart. `$F` = `%1111` -- From there you can split __BASE 2__ `%1111 1111` to look like `%111 111 111` and using the conversion `&7` = `%111` you can convert this __BASE 2__ to __BASE 8__ `&777` +- The __BASE 16__ number `$FF` converts to __BASE 8__ `377`. +- First, we convert hexadecimal to binary: + + ``` + $F = %1111 + $FF = %1111 1111 + ``` + +- Now we convert to decimal: + + ``` + 1 × 2^7 + 1 × 2^6 + 1 × 2^5 + 1 × 2^4 + 1 × 2^3 + 1 × 2^2 + 1 × 2^1 + 1 × 2^0 = 255 + ``` + +- Now we convert 255 from __BASE 10__ to __BASE 8__ by dividing by 8: + + ``` + 255 ÷ 8 = 31 remainder 7 + 31 ÷ 8 = 3 remainder 7 + 3 ÷ 8 = 0 remainder 3 + ``` + + Reading from bottom to top gives the final result: `377`. ### Answer 3 --- - I would suggest converting the __BASE 16__ number `$37` to __BASE 2__ which results in `%0011 0111`.