program DivisibleByFive;
{$mode objfpc}
{
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) mod 5
}
function IsDivisibleByFive(const bin: string): boolean;
var
remainder: integer;
i: integer;
b: integer;
begin
remainder := 0;
{ scan each bit of the binary number }
for i := 1 to Length(bin) do
begin
{ convert '0' or '1' to integer 0 or 1 }
b := Ord(bin[i]) - Ord('0');
{ update remainder using modulo arithmetic }
remainder := (remainder * 2 + b) mod 5;
end;
{ divisible if final remainder is zero }
Result := (remainder = 0);
end;
var
bin: string;
divisible: boolean;
begin
{ read an n-bit binary number as a string }
bin := '01000110'; { 70 }
divisible := IsDivisibleByFive(bin);
WriteLn('Binary number: ', bin);
if divisible then
WriteLn('Divisible by 5: yes')
else
WriteLn('Divisible by 5: no');
{
Example walk-through for bin = 01000110:
Start: remainder = 0
bit = 0 → remainder = (0*2 + 0) mod 5 = 0
bit = 1 → remainder = (0*2 + 1) mod 5 = 1
bit = 0 → remainder = (1*2 + 0) mod 5 = 2
bit = 0 → remainder = (2*2 + 0) mod 5 = 4
bit = 0 → remainder = (4*2 + 0) mod 5 = 3
bit = 1 → remainder = (3*2 + 1) mod 5 = 2
bit = 1 → remainder = (2*2 + 1) mod 5 = 0
bit = 0 → remainder = (0*2 + 0) mod 5 = 0
Final remainder = 0 → divisible by 5
}
end.
{
run:
Binary number: 01000110
Divisible by 5: yes
}
