binary division

Division is the long-division you did by hand: at each step you ask whether the divisor fits into the current portion of the dividend, write a quotient digit, subtract if it fits, then bring down the next digit. Binary makes the 'how many times does it fit' question trivial — the answer is only ever 0 or 1 — but it does not make division fast, because that yes/no decision at each step depends on the subtraction at the previous step, so the work is stubbornly sequential.

The restoring algorithm follows long division literally: shift the remainder left, subtract the divisor, and look at the sign. If the result is non-negative the divisor fit, so the quotient bit is 1 and you keep the subtraction. If it went negative the divisor did not fit, so the quotient bit is 0 and you must restore — add the divisor back to undo the trial subtraction. That restoring add is wasted work. The non-restoring algorithm is the common improvement: it does not undo a failed subtraction; instead it remembers it went negative and, on the next step, adds the divisor rather than subtracting. This removes the restore step and gives a fixed one add-or-subtract per quotient bit, at the cost of a small correction at the very end.

This is why division is the slow arithmetic operation. Add and subtract finish in a fraction of a cycle; a well-built multiplier finishes in a few cycles; but a straightforward divider needs roughly one iteration per result bit — dozens of cycles for a 64-bit divide — because each quotient bit depends on the previous remainder. Faster dividers exist (SRT division retires several bits per step using lookup tables; Newton-Raphson and Goldschmidt methods compute a reciprocal by multiplication and converge in a handful of multiply steps), but they are intricate, so designers often accept that divide is rare and let it be slow rather than spend large area making it fast.