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One of the simplest algorithm for binary numbers multiplication.The concept and the theory of the booth algorithm is explained fine on Wikipedia and here.That's why I am just giving here a simple code in C# for the booth multiplication of 2 4 bits binary numbers.
using System;
using System.Collections.Generic;
using System.Text;
namespace Booth_s_Algorithm
{
class Program
{
static void Main(string[] args)
{
string A = "0000";
string M, Q;
string Q_1 = "0";
Console.Write("Please enter a 4 bit Multiplicant = ");
M = Console.ReadLine();
Console.Write("Please enter a 4 bit Multiplier = ");
Q = Console.ReadLine();
for (int i = 0; i < 4; i++)
{
string Qo_Q = Q[3] + Q_1;
if (Qo_Q == "11" || Qo_Q == "00")
{
//shift
Q_1 = Q[3].ToString();
string NewQ = A[3].ToString() + Q[0] + Q[1] + Q[2];
Q = NewQ;
string NewA = A[0].ToString() + A[0].ToString() + A[1].ToString() + A[2].ToString();
A = NewA;
}
else if (Qo_Q == "01")
{
A = Add(A, M);
Q_1 = Q[3].ToString();
string NewQ = A[3].ToString() + Q[0] + Q[1] + Q[2];
Q = NewQ;
string NewA = A[0].ToString() + A[0].ToString() + A[1].ToString() + A[2].ToString();
A = NewA;
}
else if (Qo_Q == "10")
{
A = Subtract(A, M);
Q_1 = Q[3].ToString();
string NewQ = A[3].ToString() + Q[0] + Q[1] + Q[2];
Q = NewQ;
string NewA = A[0].ToString() + A[0].ToString() + A[1].ToString() + A[2].ToString();
A = NewA;
}
}
Console.WriteLine("\n\nA = {0}, Q = {1}, Q_1 = {2} ", A, Q, Q_1);
}
static string Add(string A, string M)
{
string answer;
string carry = "0";
string bin0 = "0", bin1 = "0", bin2 = "0", bin3 = "0";
for (int i = 3; i >= 0; i--)
{
if (A[i] == '0' && M[i] == '0' && carry == "0")
{
if (i == 3)
bin3 = "0";
else
if (i == 2)
bin2 = "0";
else
if (i == 1)
bin1 = "0";
else
if (i == 0)
bin0 = "0";
}
else
if (A[i] == '0' && M[i] == '1' && carry == "0")
{
if (i == 3)
bin3 = "1";
else
if (i == 2)
bin3 = "1";
else
if (i == 1)
bin2 = "1";
else
if (i == 0)
bin1 = "1";
}
else
if (A[i] == '1' && M[i] == '0' && carry == "0")
{
if (i == 3)
bin3 = "1";
else
if (i == 2)
bin2 = "1";
else
if (i == 1)
bin1 = "1";
else
if (i == 0)
bin0 = "1";
}
else
if (A[i] == '0' && M[i] == '0' && carry == "1")
{
carry = "0";
if (i == 3)
bin3 = "1";
else
if (i == 2)
bin2 = "1";
else
if (i == 1)
bin1 = "1";
else
if (i == 0)
bin0 = "1";
}
else
if (A[i] == '0' && M[i] == '1' && carry == "1")
{
carry = "1";
if (i == 3)
bin3 = "0";
else
if (i == 2)
bin2 = "0";
else
if (i == 1)
bin1 = "0";
else
if (i == 0)
bin0 = "0";
}
else
if (A[i] == '1' && M[i] == '0' && carry == "1")
{
carry = "1";
if (i == 3)
bin3 = "0";
else
if (i == 2)
bin2 = "0";
else
if (i == 1)
bin1 = "0";
else
if (i == 0)
bin0 = "0";
}
else if (A[i] == '1' && M[i] == '1' && carry == "0")
{
carry = "1";
if (i == 3)
bin3 = "0";
else
if (i == 2)
bin2 = "0";
else
if (i == 1)
bin1 = "0";
else
if (i == 0)
bin0 = "0";
}
else if (A[i] == '1' && M[i] == '1' && carry == "1")
{
carry = "1";
if (i == 3)
bin3 = "1";
else
if (i == 2)
bin2 = "1";
else
if (i == 1)
bin1 = "1";
else
if (i == 0)
bin0 = "1";
}
}
answer = bin0 + bin1 + bin2 + bin3;
return answer;
}
static string Subtract(string A, string M)
{
bool shift = false;
char bin3 = '0', bin2 = '0', bin1 = '0', bin0 = '0';
for (int i = 3; i >= 0; i--)
{
if (shift)
{
if (M[i] == '0')
{
if (i == 3)
bin3 = '1';
else if (i == 2)
bin2 = '1';
else if (i == 1)
bin1 = '1';
else if (i == 0)
bin0 = '1';
}
else
if (M[i] == '1')
{
if (i == 3)
bin3 = '0';
else if (i == 2)
bin2 = '0';
else if (i == 1)
bin1 = '0';
else if (i == 0)
bin0 = '0';
}
}
else
{
if (M[i] == '1')
{
if (i == 3)
bin3 = '1';
else if (i == 2)
bin2 = '1';
else if (i == 1)
bin1 = '1';
else if (i == 0)
bin0 = '1';
}
else
if (M[i] == '0')
{
if (i == 3)
bin3 = '0';
else if (i == 2)
bin2 = '0';
else if (i == 1)
bin1 = '0';
else if (i == 0)
bin0 = '0';
}
}
if (M[i] == '1')
shift = true;
}
string ans = bin0.ToString()+bin1.ToString()+bin2.ToString()+bin3.ToString();
return ans;
}
}
}
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