Consider the problem of multiplying two 4-bit unsigned integers, X=11 and Y=5, to find the product X*Y = 55. The process is outlined below:

X 1011

x Y x 0101 Reset Accum 00000000

--------

1011 Add to Accum 00001011

00000 shl 1, Add to Accum 00001011

101100 shl 2, Add to Accum 00110111

0000000 shl 3, Add to Accum 00110111 = 55₁₀

In the example above we have written the bits for X and Y so that the multiplier (Y) bits are located directly under the multiplicand (X) bits. The multiplication process begins by initializing (resetting) an Accumulator to the value 0. Note that the size of the Accumulator is 8-bits; this size of accumulator will be needed to obtain the final product result. Next, we examine the loworder, or rightmost, bit of Y. This bit has value 1 and it is multiplying the entire set of X bits. This simple product (1011) is written below. This value is added to the Accumulator. This step is followed by 4-1=3 additional steps in which the next bit of Y (proceeding right to left) is examined and if it is a 0, the product is 0, whereas if it is a 1, the product is 1011. For each of these interim products, the value is shifted to the left (shl) by the position of the Y-digit just used, then added to the Accumulator. Thus, we note that the second Y-bit is 0, hence the product is 0 and it is shifted 1 time to the left, producing the string 00000 (note 5 bits). The next Y-bit is 1 and the product is placed in the 3d line, then shifted 2 times to the left to obtain 101100 (note, 6 bits). The last Y-bit is 0 so the product, shifted by 3 bit positions to the left, is 0000000 (note, 7 bits). Each of these shifted strings are added to the Accumulator to produce the final sum 00110111 which just equals 5510. Design a multiplication circuit that accepts two L-bit unsigned binary number inputs of two registers, R1 and R2, each of length L bits, and produces output in a designated register PR (i.e. product register) of length 2L bits. Students are encouraged to do additional research (both from the textbook and also from online sources) before writing up their results to be submitted, but the solution should be relatively original and well-justified through explanation of the results. For simplicity, it is assumed that the contents of R1 and R2 are both unsigned binary numbers assume for the sake of practicality that L=32 bits, but your answer should be general to L-bit registers and 2L-bit products. Thus, the designated register PR has 2L = 64 bits. In general, it is the case that the largest possible product can be accommodated within 2L bits. Further, assume that before the multiplication circuit is enabled, both R1 and R2 have been loaded with their respective multiplier and multiplicand values (i.e. loading from RAM has already occurred). For this assignment you will design the multiplier circuit and any required additional supporting circuitry, but from the viewpoint of register transfer language and micro-operations. The complete circuit will be specified using RTL. This implies that the various timing, or control, steps of the circuit will constitute the conditions that must apply for each step to occur, in the correct order, and the set of micro-operations that will be performed at each step. Whereas the sample calculation above used a specific number of stages to the multiplication operation, it should be noted that using RTL permits significant reduction in the stated complexity of the circuit for this assignment (carefully consider the control conditions for each RTL statement). In your design approach, you will need additional components and/or circuits, such as flip-flops, counters and so on. In your submission of your work it is required that all such components, and also all assumptions, must be fully (but briefly) explained, either verbally and/or using diagrams (highly recommended that diagrams be used). The final product result should be left in the SL-bit register PR. The original contents of R1 and R2 must be left intact.