This assignment deals with implementation of a sequential multiplier in Verilog HDL.
Multiplication
This basically refers to the "long form" multiplication as we learn in school. For each digit of the multiplier, we shift the multiplicand to the appropriate place value, and then add all the partial products. An example of the partial products in binary for a simple 4-bit multiplication are shown below. As expected, multiplying two 4-bit numbers can result in an output that is up to 8 bits in length.
```
0110 # Decimal 6 - Multiplicand
x 0011 # Decimal 3 - Multiplier
--------
0110 # Partial product 0 (PP0)
0110 # PP1
0000 # PP2
0000 # PP3
--------
00010010 # Decimal 18
--------
```
### Number representation
The numbers themselves are represented in 2's complement notation. Therefore, if the multiplicand is negative, the PP values should be "sign-extended" to get the correct result. An example for negative multiplicand is shown below - negative multiplier requires similar careful handling, and is left as an exercise.
```
1010 # Decimal -6
x 0011 # Decimal 3
--------
11111010 # Partial product 0 (PP0) - sign extended
1111010 # PP1
000000 # PP2
00000 # PP3
--------
(1)11101110 # Decimal -18 (discard the overflow 1)
--------
```
### Hardware implementation
The above multiplication process can be directly implemented as combinational logic, where each partial product vector is created using a set of AND gates, and the results are put through a chain of adders.
The other alternative is to have a reduced hardware with a single register to hold the final product. This **accumulates** the final product by iterating over several clock cycles (how many?). A diagram indicating the architecture is shown here.
