# Digital Circuits: Combinational Logic Design

Digital Circuits: Combinational Logic Design
The maximum number of marks for this assignment is 40. It will contribute towards 2% of your
assessment in this subject. For Question 4 you will design a decoder for the (7,4) Hamming
code. This is the circuit that you will implement and test in Workshop 3 with in-workshop
assessment worth 4% based on the successful demonstration and understanding of your design.
I suggest that you prioritise Question 4 for this reason.
Before we begin we will define some terminology and notation that will be used in the assignment.
An n-variable minterm is a product term with each of the n variables appearing exactly
once, in complemented or uncomplemented form. There are 2n
such product terms. Examples
of 4-variable minterms are WXY Z, W XY Z and W XY Z. The product term WX Z is not a
4-variable minterm since the term does not contain Y or Y .
When you move from a truth-table to a sum-of-products expression, you are actually expressing
the function as a sum-of-minterms. We will call the minterm associated with row i of the truthtable,
minterm i (assuming that we start at row 0). A compact way of representing a function
is simply to list the minterms corresponding to the rows of the truth-table that result in an
output of 1. We do this using the notation
F(X, Y, Z) = X,Y,Z(1, 2, 4, 7)
X Y Z + XY Z + XY Z + XY Z.
Another example of this notation is
G(W, X, Y, Z) = W,X,Y,Z(5, 11, 13, 14)
W XY Z + WXY Z + W XY Z + W XY Z.
If there are some inputs for which we dont care about the corresponding output, rows 3 and 5
for example, then we will write d(3, 5) to denote this.
1. 8 marks in total (Based on Wakerly, Problem 4.19)
Using Karnaugh maps, find a minimal sum-of-products expression for each of the following
logic functions.
(a) 2 marks Fa = W,X,Y,Z(0, 1, 3, 5, 14) + d(8, 15)
(b) 2 marks Fb = W,X,Y,Z(0, 1, 2, 8, 11) + d(3, 9, 15)
1
(c) 2 marks Fc = A,B,C,D(1, 5, 9, 14, 15) + d(11)
(d) 2 marks Fd = W,X,Y,Z(3, 5, 6, 7, 13) + d(1, 2, 4, 12, 15)
2. 8 marks in total
Two functions F and G are dependent on the four Boolean variables A, B, C and D.
The functions are defined by the following expressions:
F = A,B,C,D(0, 1, 2, 3, 5, 7)
G = A,B,C,D(5, 7, 12, 13, 14, 15)
(a) 2 marks Construct the K-map for F and derive a sum-of-products expression for
F that has the fewest possible product terms.
(b) 2 marks Construct the K-map for G and derive a sum-of-products expression for
G that has the fewest possible product terms.
(c) 4 marks Revisit the K-maps for F and G and see if you can produce an implementation
that requires fewer product terms in total (and thus fewer AND gates).
3. 8 marks in total
Programmable logic devices (PLDs) have an AND-OR array for easy implementation of
sum-of-products expressions. Most PLDs have a programmable inverter/buffer at the
output of the OR gate which can be programmed to invert or not. This means that to
implement a function F we can form a sum-of-products expression for F and not invert
the OR gate output. Alternatively, we can find a sum-of-products expression for the
complement of F (F) and then invert the OR gate output.
Consider the function F = W,X,Y,Z(2, 3, 4, 5, 6, 7, 11, 13, 15). Investigate the cost (in
terms of AND gates) of each of the strategies discussed above for implementing F. This
involves finding the minimal sum-of-products expressions for F and then F and comparing
the number of product terms required in each case

# Our Service Charter

1. ### Excellent Quality / 100% Plagiarism-Free

We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions

We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure

We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee

If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.

We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

or

Instant Quote