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3 years ago

The sum of all the minterms of a boolean function of n variables is equal to 1.

Computers and Technology

1 answer:

Aleksandr-060686 [28]3 years ago

4 0

The answers are as follows:

a) F(A, B, C) = A'B'C' + A'B'C + A'BC' + A'BC + AB'C' + AB'C + ABC' + ABC

= A'(B'C' + B'C + BC' + BC) + A((B'C' + B'C + BC' + BC)

= (A' + A)(B'C' + B'C + BC' + BC) = B'C' + B'C + BC' + BC

= B'(C' + C) + B(C' + C) = B' + B = 1

b) F(x1, x2, x3, ..., xn) = ∑mi has 2n/2 minterms with x1 and 2n/2 minterms

with x'1, which can be factored and removed as in (a). The remaining 2n1

product terms will have 2n-1/2 minterms with x2 and 2n-1/2 minterms

with x'2, which and be factored to remove x2 and x'2, continue this

process until the last term is left and xn + x'n = 1

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What character makes an assignment statement an assignment statement?

Anuta_ua [19.1K]

Answer:

'='

Explanation:

The equal ('=') is the character that is used to assign the value in the programming.

In the programming, there is a lot of character which has different meaning and uses for a different purpose.

like '==' it is used for checking equality between the Boolean.

'+' is a character that is used for adding.

'-' is a character that is used for subtraction.

similarly, '=' used for assigning.

for example:

a = a + b;

In the programming, the program evaluates the (a + b) first and then the result assigns to the variable.

7 0

3 years ago

Find the inverse function of f(x)= 1+squareroot of 1+2x

Svetllana [295]

Answer:

Therefore the inverse function of $f(x)=1+\sqrt{1+2x}$ is $\frac{x^2-2x}{2}$

Explanation:

We need to find the inverse of function $f(x)=1+\sqrt{1+2x}$

Function Inverse definition :

$\mathrm{If\:a\:function\:f\left(x\right)\:is\:mapping\:x\:to\:y,\:then\:the\:inverse\:functionof\:f\left(x\right)\:maps\:y\:back\:to\:x.}$

$y=1+\sqrt{1+2x}$ $\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y$

$x=1+\sqrt{1+2y}$

$\mathrm{Solve}\:x=1+\sqrt{1+2y}\:\mathrm{for}\:y$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+\sqrt{1+2y}-1=x-1$

Simplify

$\sqrt{1+2y}=x-1$

$\mathrm{Square\:both\:sides}$

$\left(\sqrt{1+2y}\right)^2=\left(x-1\right)^2$

$\mathrm{Expand\:}\left(\sqrt{1+2y}\right)^2:\quad 1+2y$

$\mathrm{Expand\:}\left(x-1\right)^2:\quad x^2-2x+1$

$1+2y=x^2-2x+1$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+2y-1=x^2-2x+1-1$

$\mathrm{Simplify}$

$2y=x^2-2x$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\frac{2y}{2}=\frac{x^2}{2}-\frac{2x}{2}$

$\mathrm{Simplify}$

$y=\frac{x^2-2x}{2}$

Therefore the inverse function of $f(x)=1+\sqrt{1+2x}$ is $\frac{x^2-2x}{2}$

4 0

2 years ago

An enhancement to a computer accelerates some mode of execution by a factor of 10. The enhanced mode is used 50% of the time, me

Ann [662]

Answer:

The answer is "5.5 and 90.90%"

Explanation:

For point 1:

To calculate the speed from fast mode, its run time without enhancement should be worked out. Designers are aware of which two selves are implicated throughout the accelerated project planning: the empty ( $50 \%$ ) and the increased stages ( $50 \%$ ).

Although not enhanced, this would take almost as long ( $50 \%$ ) and for the combine to give phase; even so, the increased phase would've been 10 times longer, as well as $500 \%$ . Thus the corresponding total speed without enhancement is $=50\% + 500\% = 550\%.$

Its overall speed is:

$=\frac{\text{Accelerated runtime}}{ \text{accelerated runtime}} = \frac{550 \%}{ 100 \%}= 5.5$

For point 2:

We re-connect these figures in Amdahl's Law throughout order to identify how long it would take for both the initial implementation:

$\text{Vectorized fraction}= \frac{\text{Overall velocity}\times \text{Accelerated acceleration}-\text{Accelerated acceleration}}{\text{Overall acceleration} \times \text{Accelerated acceleration}-\text{Overall acceleration}}$