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3 years ago

Can someone teach me how to find all valid minterms of any given truth table?

Engineering

1 answer:

gogolik [260]3 years ago

3 0

Explanation:

A minterm is a product of variables, in which each variable appears exactly once, either complemented or not. When a truth table is represented in a sum of products form, there is one minterm for each line in the table for which the output is True (1).

Suppose I have a truth table as follows, with inputs A, B and output Z.

00 1

01 0

10 1

11 0

When I write the minterms, I use a complemented variable where the input is 0, and an uncomplemented variable where the input is 1. The minterm is expressed as a product of those variables.

Here, there are 2 lines in the table with outputs Z=1. The input conditions AB for those outputs are 00 and 10, so the corresponding minterms are A'B' and AB', where the apostrophe indicates the variable is complemented.

This table is then represented by the sum of products ...

Z = A'B' + AB'

You have all of the valid minterms when you have one for each line of the table where the output is 1.

<em>Comment on truth table representation</em>

Truth tables can be represented a number of ways. A nice representation for the purpose of identifying minterms is a list of the output for every possible combination of inputs. We have used that form above.

Sometimes, you may see minterms listed as decimal numbers in the range of 0 to 2^n -1 when there are n input variables. Then, the minterms are developed from the binary equivalents of those decimal numbers.

<u>Example</u>:

Logic with 4 input variables has minterms 7, 8, and 15. The binary equivalents of these numbers are 0111, 1000, 1111. The corresponding minterms (for inputs a, b, c, d) are a'bcd + ab'c'd' + abcd = z. Three numbers are listed, so we know we have all of the valid minterms when we have three corresponding minterms.

<em>Additional comment</em>

In some cases, outputs will be listed as "don't care." Another set of minterms can be generated for the don't cares. These can be used in the logic minimization process.

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2 years ago

2. What is the original length of the rectangular bar if the deformation is 0.005 in with a force of 1000 lbs and an area of 0.7

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Answer:

18.75in

Explanation:

Modulus of elasticity = Stress/Strain

Since stress = Force/Area

Given

Force = 1000lb

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Stress = 1000/0.75

Stress = 1333.33lbsqin

Strain

Strain = Stress/Modulus of elasticity

Strain = 1333.33/5,000,000

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Also

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3 years ago

1.8 A water flow of 4.5 slug/s at 60 F enters the condenser of steam turbine and leaves at 140 F. Determine the heat transfer ra

Ann [662]

Answer:

$Hr=4.2*10^7\ btu/hr$

Explanation:

From the question we are told that:

Water flow Rate $R=4.5slug/s=144.78ib/sec$

Initial Temperature $T_1=60 \textdegree F$

Final Temperature $T_2=140 \textdegree F$

Let

Specific heat of water $\gamma= 1$

And

$\triangle T= 140-60$

$\triangle T= 80\ Deg.F$

Generally the equation for Heat transfer rate of water $H_r$ is mathematically given by

Heat transfer rate to water= mass flow rate* specific heat* change in temperature

$H_r=R* \gamma*\triangle T$

$H_r=144.78*80*1$

$H_r=11582.4\ btu/sec$

Therefore

$H_r=11582.4\ btu/sec*3600$

$Hr=4.2*10^7\ btu/hr$

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3 years ago

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bixtya [17]

Answer:

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3 years ago

Read 2 more answers

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Ilia_Sergeevich [38]

Answer:

The heat flow in 24 hours through the refrigerator door is approximately 1,608.57 BTU

Explanation:

The given parameters are;

The duration of the heat transfer, t = 24 hours = 86,400 seconds

The area of the refrigerator door, A = 30.0" × 58.0" = 1,740 in.² = 1.122578 m²

The material of the insulator in the door = Cellulose fiber

The thickness of the insulator in the door, d = 2.0" = 0.0508 m

The temperature inside the fridge = 38° F = 276.4833 K

The temperature of the room = 78°F = 298.7056 K

The thermal conductivity of cellulose fiber = 0.040 W/(m·K)

By Fourier's law, the heat flow through a by conduction material is given by the following formula;

$\dfrac{Q}{t} = \dfrac{k \cdot A \cdot (T_2 - T_1) }{d}$

$Q = \dfrac{k \cdot A \cdot (T_2 - T_1) }{d} \times t$

Therefore, we have;

$Q = \dfrac{0.04 \times 1.122578 \times (298.7056 - 276.4833 ) }{0.0508} \times 86,400 =1,697,131.73522$

The heat flow in 24 hours through the refrigerator door, Q = 1,697,131.73522 J = 1,608.5705140685 BTU

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