# function to compute whether a binary number is divisible by 5
# it processes the bits left to right and keeps track of the remainder modulo 5
# for each bit b:
# remainder = (remainder * 2 + b) % 5
def is_divisible_by_five(bin_str: str) -> bool:
remainder: int = 0
# scan each bit of the binary number
for bit in bin_str:
# convert '0' or '1' to integer 0 or 1
b: int = int(bit)
# update remainder using modulo arithmetic
remainder = (remainder * 2 + b) % 5
# divisible if final remainder is zero
return remainder == 0
# read an n-bit binary number as a string
bin_str: str = "01000110" # 70
divisible: bool = is_divisible_by_five(bin_str)
print("Binary number:", bin_str)
print("Divisible by 5:", "yes" if divisible else "no")
"""
Example walk-through for bin = 01000110:
Start: remainder = 0
bit = 0 → remainder = (0*2 + 0) % 5 = 0
bit = 1 → remainder = (0*2 + 1) % 5 = 1
bit = 0 → remainder = (1*2 + 0) % 5 = 2
bit = 0 → remainder = (2*2 + 0) % 5 = 4
bit = 0 → remainder = (4*2 + 0) % 5 = 3
bit = 1 → remainder = (3*2 + 1) % 5 = 2
bit = 1 → remainder = (2*2 + 1) % 5 = 0
bit = 0 → remainder = (0*2 + 0) % 5 = 0
Final remainder = 0 → divisible by 5
"""
"""
run:
Binary number: 01000110
Divisible by 5: yes
"""
