In the previous article, we have already discussed the Restoring Division Algorithm. In this article, we will discuss the implementation of this algorithm.
Restoring Division Algorithm is used to divide two unsigned integers. This algorithm is used in Computer Organization and Architecture. This algorithm is called restoring because it restores the value of Accumulator(A) after each or some iterations. There is one more type i.e. Non-Restoring Division Algorithm in which value of A is not restored. Let the dividend Q = 0110 and the divisor M = 0100. The following table demonstrates the step by step solution for the given values:
| Accumulator-A(0) | Dividend-Q(6) | Status | |
|---|---|---|---|
| Initial Values | 0000 | 0110 | 0100 |
| Step 1: Left-Shift | 0000 | 110_ | |
| A – M | 1100 | Unsuccessful(-ve) | |
| Restoration | 0000 | 1100 | |
| Step 2: Left-Shift | 0001 | 100_ | |
| A – M | 1101 | Unsuccessful(-ve) | |
| Restoration | 0001 | 1000 | |
| Step 3: Left-Shift | 0011 | 000_ | |
| A – M | 1111 | Unsuccessful(-ve) | |
| Restoration | 0011 | 0000 | |
| Step 4: Left-Shift | 0110 | 000_ | |
| A – M | 0010 | 0001 | Successful(+ve) |
| Remainder(2) | Quotient(1) |
Approach: From the above solution, the idea is to observe that the number of steps required to compute the required quotient and remainder is equal to the number of bits in the dividend. Initially, let the dividend be Q and the divisor be M and the accumulator A = 0. Therefore:
- At each step, left shift the dividend by 1 position.
- Subtract the divisor from A(A – M).
- If the result is positive, then the step is said to be successful. In this case, the quotient bit will be “1” and the restoration is not required.
- If the result is negative, then the step is said to be unsuccessful. In this case, the quotient bit will be “0” and restoration is required.
- Repeat the above steps for all the bits of the dividend.
Note: Here, restoration is performed by adding back the divisor to A.
# Python program to divide two # unsigned integers using # Restoring Division Algorithm # Function to add two binary numbers def add(A, M): carry = 0 Sum = '' # Iterating through the number # A. Here, it is assumed that # the length of both the numbers # is same for i in range (len(A)-1, -1, -1): # Adding the values at both # the indices along with the # carry temp = int(A[i]) + int(M[i]) + carry # If the binary number exceeds 1 if (temp>1): Sum += str(temp % 2) carry = 1 else: Sum += str(temp) carry = 0 # Returning the sum from # MSB to LSB return Sum[::-1] # Function to find the compliment # of the given binary number def compliment(m): M = '' # Iterating through the number for i in range (0, len(m)): # Computing the compliment M += str((int(m[i]) + 1) % 2) # Adding 1 to the computed # value M = add(M, '0001') return M # Function to find the quotient # and remainder using the # Restoring Division Algorithm def restoringDivision(Q, M, A): # Computing the length of the # number count = len(M) # Printing the initial values # of the accumulator, dividend # and divisor print ('Initial Values: A:', A, ' Q:', Q, ' M:', M) # The number of steps is equal to the # length of the binary number while (count): # Printing the values at every step print ("\nstep:", len(M)-count + 1, end = '') # Step1: Left Shift, assigning LSB of Q # to MSB of A. print (' Left Shift and Subtract: ', end = '') A = A[1:] + Q[0] # Step2: Subtract the Divisor from A # (Perform A - M). comp_M = compliment(M) # Taking the complement of M and # adding to A. A = add(A, comp_M) print(' A:', A) print('A:', A, ' Q:', Q[1:]+'_', end ='') if (A[0] == '1'): # The step is unsuccessful # and the quotient bit # will be '0' Q = Q[1:] + '0' print (' -Unsuccessful') # Restoration of A is required A = add(A, M) print ('A:', A, ' Q:', Q, ' -Restoration') else: # Else, the step is successful # and the quotient bit # will be '1' Q = Q[1:] + '1' print (' Successful') # No Restoration of A. print ('A:', A, ' Q:', Q, ' -No Restoration') count -= 1 # Printing the final quotient # and remainder of the given # dividend and divisor. print ('\nQuotient(Q):', Q, ' Remainder(A):', A) # Driver code if __name__ == "__main__": dividend = '0110' divisor = '0100' accumulator = '0' * len(dividend) restoringDivision(dividend, divisor, accumulator) |
Initial Values: A: 0000 Q: 0110 M: 0100 step: 1 Left Shift and Subtract: A: 1100 A: 1100 Q: 110_ -Unsuccessful A: 0000 Q: 1100 -Restoration step: 2 Left Shift and Subtract: A: 1101 A: 1101 Q: 100_ -Unsuccessful A: 0001 Q: 1000 -Restoration step: 3 Left Shift and Subtract: A: 1111 A: 1111 Q: 000_ -Unsuccessful A: 0011 Q: 0000 -Restoration step: 4 Left Shift and Subtract: A: 0010 A: 0010 Q: 000_ Successful A: 0010 Q: 0001 -No Restoration Quotient(Q): 0001 Remainder(A): 0010
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