As described in UTF-8 and in Wikipedia, UTF-8 is a popular encoding of (multi-byte) Unicode code-points into eight-bit octets.

The goal of this task is to write a encoder that takes a unicode code-point (an integer representing a unicode character) and returns a sequence of 1-4 bytes representing that character in the UTF-8 encoding.

Then you have to write the corresponding decoder that takes a sequence of 1-4 UTF-8 encoded bytes and return the corresponding unicode character.

Demonstrate the functionality of your encoder and decoder on the following five characters:

Character   Name                                  Unicode    UTF-8 encoding (hex)
---------------------------------------------------------------------------------
A           LATIN CAPITAL LETTER A                U+0041     41
ö           LATIN SMALL LETTER O WITH DIAERESIS   U+00F6     C3 B6
Ж           CYRILLIC CAPITAL LETTER ZHE           U+0416     D0 96
€           EURO SIGN                             U+20AC     E2 82 AC
𝄞           MUSICAL SYMBOL G CLEF                 U+1D11E    F0 9D 84 9E

Provided below is a reference implementation in Common Lisp.

# input: a decimal integer
# output: the corresponding binary array, most significant bit first
def binary_digits:
  if . == 0 then 0
  else [recurse( if . == 0 then empty else ./2 | floor end ) % 2]
    | reverse
    | .[1:] # remove the leading 0
  end ;
 
# Input: an array of binary digits, msb first.
def binary_to_decimal:
  reduce reverse[] as $b ({power:1, result:0};
       .result += .power * $b
       | .power *= 2)
  | .result;