Divider 
Weighting a bread loaf with restoration and without restoration 
We want to computer Q = A ÷ D. By a stoke of luck, we have available a scale, a white bread whose weight
is actually just A and a set of brass weights with values D, 2D, 4D, 8D, .... 2^{i}*D
respectively marked with 1, 2, 4, 8, ... 2^{i}. In fact D is a binary number, and 2^{i}*D is simply obtained by a shift of D. The scale compares the sum of the weights on each of the two plates ( £ or > ). 
Digit recurrence division 
Division is not frequent. Nevertheless since its execution delay is far larger than the addition or multiplication's
one, its impact in the total execution time is substantial, thus it is advisable to design dividers carefully.
with initial conditions :
When the recurrence terminates, we have Q = Q_{0} = S_{i }q_{i} * 2^{i}. R = R_{0} is the division remainder. 
A "conditional subtractor" gives the following result S: if R < D then S = R else S = R – D ; // S = R modulo D Each "SC" cell computes both the result and the carry (borrow) of the subtraction R – D. If the output carry (leftmost) equals '1' then S is assigned the result of the subtraction else S is assigned the value of R. This last case, that seems to "restore" R to its previous value is sometimes called "restoration", from which the divider's name derives. 
The "conditional subtractor" function: if R < D then S = R else S = R – D, is abstracted by its transfer function called "Robertson's diagram". To converge the division imposes moreover that 0 £ R £ 2*D. The "Robertson's diagram" also visualizes the overflow .The overflow detection logic is not included in the following divisors.

Check whether you are acquainted with the logic of the "SC" cell : if q = '0' then { co = majority ( r, d, ci ) ; s = r } // identity else { co = majority ( r, d, ci ) ; s = r Å d Å ci } // subtraction 
A "restoring" divider consists in a series of shifts and tried subtractions. It is made of a regular array of conditional subtraction "SC" cell (subtraction or identity according to a carry out q_{j} ). 
Inverse of the division 
If the restoring divider is turned upsidedown and the conditional subtractors "SC" are substituted by conditional adders "AC" ( identity or addition according to q_{j} ) the operators delivers the inverse of the division i.e. the multiplication with "remainder" : A = D * Q + R. 
Check whether you are acquainted with the logic of the "AC" cell : 2 * co + s = (q*d) + r + ci , in other words : co = majority ((q*d), r, ci ) ; s = (q*d) Å r Å ci ; 
A "nonrestoring" divider is a sequence of shifts and additions or subtractions. Is made of a regular structure of "AS" cells (addition or subtraction according to q), q is given by the signs of R and D.

The function of a row of "AS" cells is plotted by the "Robertson's Diagram" 
Check your knowledge of the logic equations of the "AS" cell: if q = '1' then 2*co + s = r + d + ci // addition if q = '1' then 2*co + s = r + 1 – d + ci // subtraction 
Fast dividers 
Three approaches are combined to realize fast dividers:

For a square Robertson's diagram, the successive partial remainders are normalized: ( R_{j} * b^{j}
) where b is the numeration radix. 