ECE 171
HM
DIGITAL CIRCUITS
LAB PROJECT: PRIMES CIRCUIT
Lab Project: Primes Circuit, 200 Points
Due Date of Primes Circuit:
Total Points:
Agreed Date to Present:
Show TA Lab Project Progress:
Extra Credit up to 25 points:
Lab with TA:
Lab with TA:
PSU
(2/6/2016)
Thursday 3/3/2016 in the lab; earlier dates to be agreed with TA
200
2/5/2016
2/18/2016
Simulating the Primes circuit using a SW tool
Fridays 14:00 – 14:50, Intel Lab, FAB base, your own laptop
Fridays 15:00 – 15:50, Intel Lab, FAB base, your own laptop
General Rule: Create your Primes lab project using an electronic tool, e.g. Microsoft Word. By
week 5 arrange a date for the final presentation in the lab with the TA. During the last few weeks,
students present completed Primes project to the TA to get full credit. Students who simulate their
Primes solution get extra credit. Students who build their Primes solution in HW get extra credit.
Students who do both get both extra credits.
Summary: Student teams design, write, document, and present a solution for a lab project, named
Primes. Primes is a combinational circuit that reads input signals, interprets them as an integer
number, and outputs a signal stating, whether or not that integer is a prime number. Only very
small, non-negative integers below 16 are considered for input. Note: 1 counts as a prime number.
Detail: Step 1: Given input lines ni = n0, n1, n2 etc., devise a truth table for Primes(). Compute i,
i.e. explain, how many input lines i are minimally needed for 16 different combinations, and why.
Integer inputs range from 0 to 15. Document your choice for i.
Step 2: Define the full, non-optimized Primes() function as a sum of products of the input variables
ni, i = 0 .. 15. Do not minimize or optimize function Primes() yet. Instead, show a complete, full sum
of products. Document function: Primes = n0’ n1’ n2’ ... + n0 n1’ n2’ ..., with the ’
standing for logical negation, and juxtaposition as “logical and” operation; e.g. “n1 n2” means: “n1
and n2”. The + operator stands for “logical or”; e.g. “n1 + n2” means: “n1 or n2”.
Step 3: Draw a complete electric circuit, using and gates, or gates, and negaters to produce the
single output signal Primes(), which is 1, only if the input lines constitute a prime number. Using
schematics capture software yields extra credit of up to 15 points.
Step 4: Reduce the Boolean function Primes() from Step 2 to a simpler, minimized function named
Primes_min(), using combinational circuit minimization techniques. Hint: if a sum of product terms
differs by only a single variable v, with v’ negated in one of the 2 terms, the sum can be replaced by
a single term with v missing. For example: t = a b c’ + a b c can be replaced by t = a b. Apply
this minimization or others successively!
Step 5: Draw a complete electric circuit, using only and gates, or gates, and not gates to produce
the single output signal Primes_min(), which is 1, only if the input lines constitute a prime number.
State the total net saving of gates in Primes_min() versus the earlier HW implementation of
Primes().
Sep 6: Draw a complete Karnaugh Map, whose variables are the input lines for Primes(). Place a 1
into the Karnaugh map if the combination of input signals can be interpreted as a prime number;
place a 0 otherwise.
Step 7: Demonstrate to the TA in the lab during one of the last few weeks.
Milestones: Teams need to agree about a final presentation date by the deadline shown in table
Lab Project Milestones. Teams show intermediate progress to Primes in the lab by the specified
date; TA signature is required. Teams present their solution using any medium (e.g. hardware
1
Lab Project
ECE 171
HM
DIGITAL CIRCUITS
LAB PROJECT: PRIMES CIRCUIT
PSU
implementation, HDL, etc.) in the lab to the TA during the last few weeks of class; TA signature
required for credit.
Lab Project Milestones



Milestone and Date
Teams using schematic capture (or CAD) tools get 15 % extra credit
Teams who build Primes() or Primes_min() circuit in hardware get 25 % extra credit
Yes, teams may do both: design using a simulation tool and also implement in
hardware, get a total of 40% extra credit
By Friday 2/5/2016, teams agree with the TA about final presentation date in the last
few weeks of class
By Friday 2/12/2016 teams have started design process for lab project
By Friday 2/19/2016 each team presents intermediate progress of lab project to the
TA in the lab; credit requires TA’s signature
Step 1: Define number of input lines, name them ni with i = 0, 1, 2, etc. show the truth
table for output Primes()
Step 2: design and document the Primes() function as a sum of products (SoP) of the
input signals
Step 3: Draw the complete circuit for Primes(); max 10 points total extra credit for use
of schematic capture program
Step 4: derive the function Primes_min(), which is an optimized (minimized) version of
Primes()
Step 5: Draw the complete circuit for Primes_min(); max 10 points total extra credit for
use of schematic capture program
Step 6: draw Karnaugh map using an electronic tool, e.g. MS Word or MS Excel etc.;
not to be hand-drawn
Step 7: By Friday 3/4/2016 all teams have demonstrated their completed lab project
(electronic tool such as MS Word to draw circuit; or Verilog or similar tool) to the TA;
credit requires TA’s signature
Total
2
Lab Project
Points
5
n/a
25
20
20
20
20
20
20
50
200