- The Most Significant Bit (MSB) of "Q" is should be assigned as the Least Significant Bit (LSB) of "R" while left shifting "RQ".
- After left shifting of "RQ", there should be a statement to update "R" based on its signed bit, either by adding or subtracting "D".
- After updating "R", the LSB of Q should be updated depending on the signed bit of R.
- Since this algorithm involves many bitwise operations like left shift, right shift, and bitwise assignment, it is recommended to use arrays to represent binary numbers instead of decimal numbers.

# Incorrect non restoring division for unsigned integers !!

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Hi there,

For unsigned integer values, I am attempting to construct a non-restoring division algorithm, but it appears that I am having difficulties getting the quotient and remainder right.

Can you give me some advice on how to improve the implementation?

Many thanks

clearvars;clc;

n = 32;

N = 11;

D = 3;

R = zeros(1,1);

Q = 0;

D = bitshift(D, 1);

for i = 1 : (n-1) %.. 0 do -- for example 31..0 for 32 bits

if R >= 0

Q = accumpos(Q,1);

R = 2 * R - D;

else

Q = accumneg(Q,1);

R = 2 * R + D;

end

end

Q = Q - not(Q); % -- Appropriate if −1 digits in Q are represented as zeros as is common.

if R < 0

Q = accumneg(Q,1);

R = R + D; %-- Needed only if the remainder is of interest.

end

Q ,R

##### 0 Comments

### Answers (1)

Yash
on 7 Sep 2023

Edited: Yash
on 12 Sep 2023

Hi,

I can understand that you are interested in implementing the non-restoring division for unsigned integers.

I have reviewed your code and noticed a few areas that require attention:

Kindly refer to the below example code snippet that demonstrates how to initialize the arrays using binary representations:

dividendBin = dec2bin(dividend);

divisorBin = dec2bin(divisor);

% Initialize the registers

A = zeros(1, numBits+1);

Q = zeros(1, numBits);

% Set the dividend and divisor in the registers

Q(end-length(dividendBin)+1:end) = dividendBin - '0';

M = [zeros(1, numBits - length(divisorBin)+1) divisorBin-'0'];

Refer the below code to implement the algorithm:

for i = 1:numBits

% Check signed bit of A

A0 = A(1);

%left Shift AQ

A = [A(2:end) Q(1)];

Q = [Q(2:end) 0];

if A0==0

A = addBin(A,negM);

else

A = addBin(A,M);

end

% Decide LSB of Q

if(A(1)==1)

Q(end)=0;

else

Q(end)=1;

end

end

quotient = bin2dec(num2str(Q));

remainder = bin2dec(num2str(A));

In the above example, "addBin" is a custom MATLAB function which adds two arrays containing binary representations, "negM" is the 2's complement of M.

I hope this helps you address the issue.

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