Purpose
Review system-level design by designing, functionally verifying, and FPGA prototyping a digital system for accelerating the factorial computation. The system should start execution upon receiving an external input “Go” and should output a “Done” signal when the execution is completed. In addition, an “Error” signal should be set when an input greater than 12 is entered.
Background
1) The algorithm for computing the factorial of n, i.e., n! = 1 x 2 x … x n, is shown below:
INPUT n
product = 1
WHILE (n > 1) {
product = product * n
n = n -1
}
OUTPUT product
Figure 1. The Factorial of n Algorithm
2) Functional building blocks to be used in building the datapath of the system is provided in Fig.2 below. CNT is a down counter with parallel load control and an enable signal; REG is a data register with a load control signal; CMP is a comparator with a GT (greater-than) output; MUL is a combinational multiplier for unsigned integers; MUX is a 2-to-1 multiplexer; BUF is a tri-state buffer for output control, but is recommended to use another 2-to-1 MUX for this purpose.
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Figure 2. Functional Building Blocks of the Factorial Datapath Module
3) The factorial accelerator shall calculate and display results up to 12! (which is 0x1C8CFC00). Inputs for n should be unsigned. Use only one of each building block in Fig. 2 to build the accelerator’s datapath (it is recommended to use a second 2-to-1 MUX to replace the output buffer BUF). In order to capture inputs that are greater than 12, an additional comparator (or some simple gate-level logic) will be needed. Except these, no other submodule should exist within the datapath. Parameterize the data path elements to make it easier for scaling the data width.
Tasks
1) Design the system’s datapath using the given building blocks
2) Draw the two-piece (CU-DP) system block diagram that shows all relevant signals
3) Draw the ASM chart which describes the cycle-by-cycle operations of the datapath
4) Draw bubble diagram for the “next state logic” (NS) part of the control unit
5) Construct an output table for the “output logic” part of the control unit
6) Based on the above, write Verilog design code for the factorial accelerator, as well as testbench code to functionally verify your design
7) Write a report based on your work, with the following requirements (this is also the standard for future reports):
(1) Cover page (you can leave the Lab Checkup Record field blank)
(2) All requirements introduced in the Lab Report Requirements & Schematic Drawing Guidelines
(3) Appendices including the following:
(a) diagrams and table mentioned in Tasks 1 – 5, generated by Visio or other tools
(b) source code for both design and verification
(c) waveforms captured from your simulation results
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