import Foundation
// 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
func isDivisibleByFive(_ bin: String) -> Bool {
// remainder modulo 5 while scanning bits
var remainder: Int = 0
// scan each bit of the binary number
for bit in bin {
// convert '0' or '1' to integer 0 or 1
let b: Int = Int(bit.asciiValue! - Character("0").asciiValue!)
// 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
let bin: String = "01000110" // 70
let divisible: Bool = isDivisibleByFive(bin)
print("Binary number: \(bin)")
print("Divisible by 5: \(divisible ? "yes" : "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
*/
