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GuDViN [60]
3 years ago
11

Design a Boolean circuit that verifies whether a given integer 0 ≤ x < 16 is divisible by 5

Mathematics
2 answers:
Dmitry_Shevchenko [17]3 years ago
8 0

This question is incomplete, the complete question is;

Your boss asks you to design a Boolean circuit that verifies whether a given integer 0 < x < 16 is divisible by 5.

Every such number is represented in binary using four bits, say b₃b₂b₁b₀, and so your Boolean circuit will have four inputs. For instance, the number 13 is written in binary as 1101 and so to test its divisibility by 5 a user would feed the values b₀ = 1, b₁ = 0, b₂ = 1, and b₃ = 1 into the inputs of your circuit.

The Boolean circuit will have a single output, which should deliver the value 1 if the iput values represent a number that is divisible by 5 and 0 otherwise.

a) write down the truth table of the Boolean function F(b₀,b₁,b₂b₃) that implements this "divisible by 5" operation

b) construct a Boolean expression in disjunctive normal form that implements the Boolean function yo wrote down in a)

Answer:

Given that;

integer range = 0≤ x ≤ 16

within 4bits, we can represnt each number

(0,5,10,15)

a)  

Truth table for function that implements  divisible by 5

Integer    B3    B2    B1    B0     Y

0              0       0      0      0      1

1              0       0      0       1      0

2              0       0      1        0     0

3              0       0      1        1      0

4              0       1       0       0     0

5              0       1       0       1      1

6              0       1       1        0     0

7              0       1       1        1       0

8              1       0      0        0      0

9              1       0      0        1       0

10             1       0      1         0      1

11              1       0      1          1      0

12             1        1      0         0     0

13             1         1     0          1      0

14             1         1       1         0     0

15            1         1        1        1       1

b)

Boolean expression that implements the Boolean function from a)

from the truth table;

Boolean expression Y is;

Y = b⁻₃b⁻₂b⁻₁b⁻₀ / y₁   +   b⁻₃b₂b⁻₁b₀ / y₂   +   b₃b⁻₂b₁b⁻₀ / y₃   +   b₃b₂b₁b₀ / y₄

alexandr402 [8]3 years ago
6 0

Answer:

  circuit is in the second attachment

Step-by-step explanation:

Attached is a truth table for the desired circuit, where b3–b0 are the input bits, MSB–LSB. We notice that the output is true whenever b3=b1 and b2=b0. This can be written in DNF as ...

  Y=b_3'b_2'b_1'b_0'+b_3b_2'b_1b_0'+b_3'b_2b_1'b_0+b_3b_2b_1b_0

More compactly, it can be written in terms of the exclusive-nor function as ...

  y=(b_3\odot b_1)\wedge(b_2\odot b_0)

A circuit diagram showing this circuit is the second attachment. (A–D are the input bits, in order MSB–LSB (or its reverse)).

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Answer:

D. All real numbers

Step-by-step explanation:

The range of a function is all of the possible x-values (which is easiest to understand if you can view a graph), and the domain of a function is all possible y-values.

So, you could put any x-value into this function (and it would have a corresponding y-value)

The domain [y] is limited, but the range [x] is best described as all real numbers

(if it's hard to remember which is which, d comes before r alphabetically, and x comes before y alphabetically)

7 0
2 years ago
Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length
liubo4ka [24]

Answer:

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Step-by-step explanation:

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Volume of a Rectangular pyramid = Length × Width × Height

From the above question

Height = Width = x

Length = 2 × Width

Length = 2x

Volume = 3,456 cubic inches

Hence,

3,456 = 2x × x × x

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x³ = 3456/2

x³ = 1728

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Cube root(x³) = cube root (1728 cubic Inches)

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3 0
3 years ago
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valentina_108 [34]

Answer:

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Step-by-step explanation:

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3 years ago
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GalinKa [24]

Answer: 40%

Step-by-step explanation:

Setting up an equation to solve,

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The equation, looking like this,

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3 0
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Answer:

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6 0
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