Question

In addition, digits are added bit by bit from right to left with the carries being passed to the next digit to the left. Subtraction uses addition although the operand is negated before being added. Multiplication and division on the other hand can be much more complex. Research how both of these operations are handled at a hardware level. Provide an explanation of the algorithms that would be used to create those calculations.

Answer 1

In addition, digits are added bit by bit from right to left with the carries being passed to the next digit to the left. Subtraction uses addition although the operand is negated before being added.
Multiplication and division on the other hand can be much more complex. Research how both of these operations are handled at a hardware level. Provide an explanation of the algorithms that would be
used to create those calculations.

Ans. In addition, digits are added bit by bit from right to left with the carries being passed to the next digit to the left. Subtraction uses addition although the operand is negated before being added.

For multiplication: Now a days electronic circuits used to multiply are called binary multipliers
The root algorithm at the basis of all sorts of electronic multipliers is repeated addition with shifting.
So that 123x321 would be realized as 123+1230+1230+12300+12300+12300.

Older multiplier architectures employed a shifter and accumulator to sum each partial product, often one partial product per cycle, trading off speed for die area. Modern multiplier architectures use the (Modified)
Baugh–Wooley algorithm,[7][8][9][10] Wallace trees, or Dadda multipliers to add the partial products together in a single cycle. The performance of the Wallace tree implementation is sometimes improved by modified
Booth encoding one of the two multiplicands, which reduces the number of partial products that must be summed.

For Division :
Integer division in computer hardware is done through subtraction and shifting of digits exactly like typical longhand division in the crudest method, while better methods use algorithms that compute the
result much quicker and in fewer steps. There are various algorithms like Restoring method and non restoring method.

Restoring and Non-restoring integer division, which are based upon the basic longhand division, however more efficient algorithms used for fast division like Newton-Raphson division and Goldschmidt
division do exist.