1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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)).

You might be interested in
{(-4, 12), (-2, 6), (0, 0), (3,-9), (7, -21)} Is this a function? Yes No How do you know? Is this proportional? Yes No How do yo
Sati [7]
Yes it is I took the test
8 0
3 years ago
6th grade math !!!!!!!!!!!!!!!
nydimaria [60]

Answer:

x=3

Step-by-step explanation:

Well if 4x>10, then x needs to be more than 2.5, (because 2.5*4=10) So the only answer left is x=3

7 0
3 years ago
Read 2 more answers
You can see Tali's current age and birth year in the table below. You will also find the
lana66690 [7]

My aunt's age is 43.

My brother's age is 16.

My mother's age is 41.

<h3>What are the current ages?</h3>

In order to determine the current ages, the year the ages are been calculated has to be determined first. The year can be determined by adding my Tali's age to the year he was born.

2008 + 13 = 2021

What is my aunt's age = 2021 - 1978 = 43

What is my brother's age = 2021 - 2005 = 16

What is my mother's age = 2021 - 1980 = 41

To learn more about subtraction, please check: brainly.com/question/854115

5 0
2 years ago
Jody decides to ride her bike from her house to the park. The distance she travels on her bike, In
grin007 [14]

Answer:

top:correct

middle:incorrect

bottom:correct

Step-by-step explanation:

4 0
2 years ago
the table shows the fraction of votes that each candidate received. if 230 students voted, how many students voted for each cand
zaharov [31]
3/5=6/10 so Naomi got 138.
Luke got 69.
And Natalie got 23.
5 0
3 years ago
Read 2 more answers
Other questions:
  • A circle has a radius of V131 units and is centered at (0, -4.3).
    9·1 answer
  • Which graph represents the division of -12 / 4 ?
    5·1 answer
  • Select the correct answer.
    7·1 answer
  • Solve for K<br><br> 3(k+5)=-2(3k-6)
    11·1 answer
  • How do you solve quadratics
    5·2 answers
  • What is the slope of a line which makes an angle of 45 degree with x-axis? *​
    12·2 answers
  • Pls help me no explanation needed ❤️❤️❤️
    10·1 answer
  • PLS HELP!!!!! ITS ALGEBRA 1!
    13·1 answer
  • Here is my question.
    8·2 answers
  • PLEASE HELP WILL GIVE BRAINLY AND 5.0 RATING
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!