mathematics

Logic redundancy

Logic redundancy is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Logic redundancy rather than just read about it. In short: Logic redundancy occurs in a logic gate network containing circuitry that does not affect the static logic function. There are several reasons why logic redundancy may exist.

Key takeaways

Logic redundancy belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Logic redundancy to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Logic redundancy from memory before moving on to harder problems.

Reference excerpt

Logic redundancy occurs in a logic gate network containing circuitry that does not affect the static logic function. There are several reasons why logic redundancy may exist. One reason is that it may have been added deliberately to suppress transient glitches (thus causing a race condition) in the output signals by having two or more product terms overlap with a third one. Consider the following equation:

Y = A B + A ¯ C + B C . {\displaystyle Y=AB+{\overline {A}}C+BC.}

The third product term B C {\displaystyle BC} is a redundant consensus term. If A {\displaystyle A} switches from 1 to 0 while B = 1 {\displaystyle B=1} and C = 1 {\displaystyle C=1} , Y {\displaystyle Y} remains 1. During the transition of signal A {\displaystyle A} in logic gates, both the first and second term may be 0 momentarily. The third term prevents a glitch since its value of 1 in this case is not affected by the transition of signal A {\displaystyle A} . Another reason for logic redundancy is poor design practices which unintentionally result in logically redundant terms. This causes an unnecessary increase in network complexity, and possibly hampering the ability to test manufactured designs using traditional test methods (single stuck-at fault models). Testing might be possible using IDDQ models.

Removing logic redundancy Logic redundancy is, in general, not desired. Redundancy, by definition, requires extra parts (in this case: logical terms) which raises the cost of implementation (either actual cost of physical parts or CPU time to process). Logic redundancy can be removed by several well-known techniques, such as Karnaugh maps, the Quine–McCluskey algorithm, and the heuristic computer method.

Adding logic redundancy

In some cases it may be desirable to add logic redundancy. One of those cases is to avoid race conditions whereby an output can fluctuate because different terms are "racing" to turn off and on. To explain this in more concrete terms the Karnaugh map to the right shows the minterms for the following function:

f ( A , B , C , D ) = E ( 6 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ) . {\displaystyle f(A,B,C,D)=E(6,8,9,10,11,12,13,14).\ }

The boxes represent the minimal AND/OR terms needed to implement this function:

f = A C ¯ + A B ¯ + B C D ¯ . {\displaystyle f=A{\overline {C}}+A{\overline {B}}+BC{\overline {D}}.}

The k-map visually shows where race conditions occur in the minimal expression by having gaps between minterms, for example, the gap between the blue and green rectangles. If the input were to change from 1110 {\displaystyle 1110} to 1010 {\displaystyle 1010} then a race will occur between B C D ¯ {\displaystyle BC{\overline {D}}} turning off and A B ¯ {\displaystyle A{\overline {B}}} turning on. If the blue term switches off before the green turns on then the output will fluctuate and may register as 0. Another race condition is between the blue and the red for transition from 1110 {\displaystyle 1110} to 1100 {\displaystyle 1100} . The race condition is removed by adding in logic redundancy. Both minterm race conditions are covered by addition of the yellow term A D ¯ {\displaystyle A{\overline {D}}} . In this case, the addition of logic redundancy has stabilized the output to avoid output fluctuations because terms are racing each other to change state.

Notes

Illustrations

Worked examples

Example 1 — a first encounter with Logic redundancy

Start with the simplest possible case. Write down what Logic redundancy claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Logic redundancy before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Logic redundancy ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Logic redundancy

In research: Logic redundancy appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Logic redundancy in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Logic redundancy is common in secondary-school and first-year university syllabi. It links to neighbouring topics Boolean algebra, Digital electronics, Electronic engineering, so understanding it makes those chapters shorter.
In everyday life: Look for Logic redundancy outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Logic redundancy in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Logic redundancy means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Logic redundancy out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Logic redundancy in simple terms?

Logic redundancy occurs in a logic gate network containing circuitry that does not affect the static logic function. There are several reasons why logic redundancy may exist.

Why does Logic redundancy matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Logic redundancy?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Logic redundancy.