Answer:
a) the K-map is in the attachment
<em>f = Σ</em>m(0,1,2,3,6,10,14,15)
b) from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
Step-by-step explanation:
A Karnaugh map (K-map) is a pictorial framework used to limit the Boolean expressions without utilizing Boolean algebra theorems and equation controls.
a) the given function is <em>f</em>(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
expanding the function as four variable terms
<em>f</em>(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
= A'B'(C + C')(D + D')+(A + A')(B + B")CD' + ABC(D + D') + A'B'CD' + ABCD'
= A'B'CD + A'B'CD' + A'B'C'D' + ABCD' +AB'CD' + A'BCD' + A'B'CD' + ABCD +ABCD' + A'B'CD' + ABCD'
=A'B'CD + A'B'CD' + A'B'C'D + A'B'C'D' + ABCD' + AB'CD' + A'BCD' +ABCD
<em>f = Σ</em>m(0,1,2,3,6,10,14,15)
note: diagram is in the attachment
b) the minterms for the minimum sum of product are
<em>f = Σ</em>m(0,1,2,3,6,10,14,15)
simplifying the K-map(done in the attachment)
from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the maxterms for the minimum product of sums are
<em>f </em>= ПM(4,5,7,8,9,11,12,13)
plot the K-map to find minimum product of sums(done in the attachment)
the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
Answer:
We are to find the error made by Sadie and then find the correct simplification.
The error Sadie made is that she wrote as
instead of
.
The square root of is
and so she could have further simplified.
The correct simplification is shown below:
Answer:
Step-by-step explanation:
From the question we are told that:
Force 1
Force 2
Force 3
Direction 1
Direction 2
Direction 3
Generally Resolving forces to X axis is mathematically given by
Generally Resolving forces to Y axis is mathematically given by
Generally the equation for Resultant force R is mathematically given by
Let's start with " times a number". We will use
to represent the number.
" less than" is next.
Finally, "is ".
Put it all together to get an expression.
Now, let's solve for the unknown number.
Add on both sides of the equation.
Divide both sides of the equation by to isolate
.