// 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
fn is_divisible_by_five(bin: &str) -> bool {
// remainder modulo 5 while scanning bits
let mut remainder: i32 = 0;
// scan each bit of the binary number
for bit in bin.chars() {
// convert '0' or '1' to integer 0 or 1
let b: i32 = bit as i32 - '0' as i32;
// update remainder using modulo arithmetic
remainder = (remainder * 2 + b) % 5;
}
// divisible if final remainder is zero
remainder == 0
}
fn main() {
// read an n-bit binary number as a string
let bin: &str = "01000110"; // 70
let divisible: bool = is_divisible_by_five(bin);
println!("Binary number: {}", bin);
println!("Divisible by 5: {}", if divisible { "yes" } 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
*/
