#convert a decimal number to a string
def num_to_string(num):
    bits = num_to_bits(num)
    return bits_to_string(bits)

def string_to_num(s):
    bits = string_to_bits(s)
    return int(bits, 2)

#converts a string to a bitstream
def string_to_bits(s):
    encoded = ""
    for ch in s:
        encoded += char_to_5bit(ch)
    return encoded

#converts a bitstream to a string
def bits_to_string(s):
    decoded = ""
    for i in range(0, len(s), 5):
        next_bits = s[i:i+5]
        ch = bits_to_char(next_bits)
        decoded += ch
    return decoded

#converts a decimal number to a string of bits
def num_to_bits(num):
    binary_string = str(format(num, 'b'))
    if len(binary_string) % 5 == 0:
        return binary_string
    else: 
        num_leading_zeros = 5 - (len(binary_string)%5)
        return '0' * num_leading_zeros + binary_string
    

punctuation_to_num = {'.': 27, ',': 28, '!': 29, "'": 30, "-": 31}
num_to_puncutation = {27: '.', 28: ',', 29: '!', 30:"'", 31: "-"}

def char_to_5bit(ch):
    """
    Converts a single character to a 5-bit binary string.
    
    """
    # Check for space first.
    if ch == ' ':
        return '00000'
    
    # Convert character to lowercase for uniform processing.
    ch = ch.lower()
    
    # If it's a letter, map it from a=1, b=2, ..., z=26.
    if 'a' <= ch <= 'z':
        num = ord(ch) - ord('a') + 1  # a -> 1, b -> 2, ..., z -> 26
        return format(num, '05b')
    
    # map punctuation to 5-bits as in punctuation_to_num
    elif ch in punctuation_to_num:
        return format(punctuation_to_num[ch], '05b')
    
    
    return ''

def bits_to_char(bits):
    if len(bits) != 5:
        print("length is wrong!")
        return ''
    try:
        num = int(bits, 2) #convert the bitstring into a decimal integer
    except ValueError:
        return ''
    
    if num == 0: #0 = space
        return ' '
    elif 1 <= num <= 26: #letters indexed by position in alphabet
        return chr(num + ord('a') + -1)
    elif num in num_to_puncutation: #map numbers to punctuation as in num_to_punctuation
        return num_to_puncutation[num]