Question

- 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)

Answer #1

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)

Expand the following expression into minterms and then simplify
it using K-map.
F(A,B,C,D) = BC'D' + A'C'D + ACD + BCD + A'BD

simplify the following boolean expresions by use of k map
a'b' + bc + a'bc'
p'qr + pq'r' + pq'r
xy' + x'y

Find the truth table (function table), SOM, POM, and
simplify the expression using K Map approach of the following Sigma
notation expression: (10 points) f(w,x d y,z)= sum
m(0,3,9,10,14,15)

(a) Implement the following Boolean function F using the
two-level forms: AND-NOR and
OR-NAND , F = B'D'+ AC'D'+ACD+A'CD'
(b) Convert the above problem into standard POS, expression using
the truth table and minimize
using K-map.
(c) Design a combinational circuit with four inputs and one output.
The Algebraic expression
must be minimized using K-MAP. The output must be one for the
digits which are present in
your Roll Number Digits. Any duplications must be avoided.

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)

f(a,b,c) =
Xm(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.

(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’)

Logic Circuit
Problem #3
Given the following logic function: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8) use a Karnaugh Map to, a) Find a
minimal SOP expression Answer: F(a,b,c,d) = b) Find a minimal POS
expression
Answer: F(a,b,c,d) =
Problem #4
Implement the function F(a,b,c,d) given in problem #3 using two
3-to-8 decoders, both active low enabled and active low output.
F(a,b,c,d) = ? m(0,3,7,9,11,13,15)+?d(4,6,8)
Answer:
Problem #5
Implement the function in the previous problem: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8), using a single 4...

1. Given a Boolean function ?(?, ?, ?) such that ?(?, ?, ?) = 1
if the binary number ??? divides 36,
and ?(?, ?, ?) = 0 otherwise:
a. Construct the Truth Table for ?(?, ?, ?)
b. Find the Sum of Products (SoP) expansion for ?(?, ?, ?)
c. Minimize the SoP from above, using the K-map, state the
minimized function
d. Draw a combinatorial circuit for the minimized function

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