Question

*f*(*a,b,c*) =
^{X}*m*(0*,*1*,*5)

Use boolean algebra to simplify both of the above expressions to
determine the *minimal sum-of-products* and the *minimal
product-of-sums* representation for the above function.

Answer #1

Use the properties and theorems of Boolean algebra to reduce the
following expressions to
AND-OR expressions without parentheses. The expressions may not be
unique. Construct the
truth table, which will be unique, by inspection of your final
expression.
g) (a ⊕ b) ⊕ c
i ) (a + b)(a′ + c)(b′ + c′)

Using K-map to simplify the following Boolean function:
F(A,B,C,D) = m(1,3,5,6,7,9,11,12,13,15)

Using K-map to simplify the following Boolean function:
F(A,B,C,D) = å
m(1,3,5,6,7,9,11,12,13,15)

The grammar below generates Boolean expressions in prefix
notation:
B → O B B | not B | id O → and | or
a) Write an attribute grammar to translate Boolean expressions
into fully parenthesized infix form. For example, expression and
and a or b c d turns into the following fully parenthesized
expression ((a and (b or c)) and d).
b) Now write an attribute grammar to translate the Boolean
expressions into parenthesized expressions in infix form without...

Find the simpliest SOP expression using boolean algebra.
F(A,B,C,D) = A’B’CD + A’BCD’ + A’BCD + AB’C’D’ + AB’C’D +
ABC’D’

G1 = (A’+C’+D) (B’+A) (A+C’+D’)
G2 = (ABC’) + (A’BC) + (ABD)
G3 = (A+C) (A+D) (A’+B+0)
G4 = (G1) (A+C)
G5 = (G1) (G2)
G6 = (G1)+(G2)
Determine the simplest product-of-sums (POS) expressions for G1
and G2.
Determine the simplest sum-of-products (SOP) expressions for G3
and G4.
Find the maxterm list forms of G1 and G2 using the
product-of-sums expressions.
Find the minterm list forms of G3 and G4 using the
sum-of-products expression.
Find the minterm list forms of...

(3) Use K-map to simplify the following expressions, and
implement them with two-level NAND gate circuits:
(a) F(A,B,C,D)=A’B’C+AC’+ACD+ACD’+A’B’D’
(b) F(A,B,C)=(A’+B’+C’)(A’+B’)(A’+C’)

Use the following expressions for left and right sums
left
sum
=
f(t0)Δt
+
f(t1)Δt
+
f(t2)Δt
+ +
f(tn −
1)Δt
right
sum
=
f(t1)Δt
+
f(t2)Δt
+
f(t3)Δt
+ +
f(tn)Δt
and the following table.
t
0
4
8
12
16
f(t)
25
22
20
18
15
(a) If n = 4, what is
Δt?
Δt =
What are
t0,
t1, t2,
t3,
t4?
t0
=
t1
=
t2
=
t3
=
t4
=
What are
f(t0),
f(t1),
f(t2),
f(t3),...

Simplify the following Boolean functions, using K-maps. Find all
the prime implicants, and determine which are essential:
(a) F (w, x, y, z) = ? (1, 4, 5, 6, 12, 14, 15)
(b) F (A, B, C, D) = ? (2, 3, 6, 7, 12, 13, 14)
(c) F (w, x, y, z) = ? (1, 3, 4, 5, 6, 7, 9, 11, 13, 15)

Given F = AB′D′ + A′B + A′C + CD.
(a) Use a Karnaugh map to find the maxterm expression for F
(express your answer
in both decimal and algebric notation).
(b) Use a Karnaugh map to find the minimum sum-of-products form
for F ′.

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