package main
import (
"fmt"
)
// 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
remainder := 0
// scan each bit of the binary number
for _, bit := range bin {
// convert '0' or '1' to integer 0 or 1
b := int(bit - '0')
// update remainder using modulo arithmetic
remainder = (remainder*2 + b) % 5
}
// divisible if final remainder is zero
return remainder == 0
}
func main() {
// read an n-bit binary number as a string
bin := "01000110" // 70
divisible := isDivisibleByFive(bin)
fmt.Println("Binary number:", bin)
fmt.Println("Divisible by 5:", func() string {
if divisible {
return "yes"
}
return "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
*/
