Question

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 input multiplexer, active low enabled. Minimize the discrete gate count at the multiplexer inputs.

Answer:

Answer #1

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 ′.

Q2: Implement F(A,B,C)=(A+B+C)(A’+C’)(B’+C’) using: (5 pts
each)
A. A 3x8 active high decoder
B. A 3x8 active low decoder
C. A 2x1 multiplexer.
D. A 4x1 multiplexer.
Q3: Implement a Full Adder using: (5 pts each)
A. A 3x8 active high decoder
B. A 3x8 active low decoder
C. With two 2x4 Active high decoders.

Mr Ali is undergraduate student of engineering in a University.
His registration ID is of six hexadecimal numbers (171457)16. He
needs to understand some useful operations in digital logic design
so he represented each character of his registration ID as a
four-bit number in a truth table of 16 input output relations. Then
he assigned HIGH output to each four-bit number of his registration
id and its succeeding number (all other outputs will then be
zero).
Your task is to...

Given the SOP function:
f(a,b,c,d) = Σ m ( 1 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 13 ) + Σ d
( 2 , 9 , 15 )
Use the Quine-McCluskey method to show that the minimum output
function, f, is:
f (a,b,c,d) = b'cd' + bc' + a'd + a'b or f(a,b,c,d) = b'cd' +
bc' + a'd + a'c

Find the minimum sum-of-products expression for the following
functions using the LogicAid Karnaugh Map Tutorial
mode:
1. f(a,b,c,d) = ?m (0,2,3,4,7,8,14)
2. f(a,b,c,d) = ?M(1,2,3,4,9,15)
3. f(a,b,c,d) = ?M(0,2,4,6,8)* ?D(1,12,9,15)

(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.

1. Implement the given logic function using a 4:1 MUX. F(A,B,C)
= Σm(0,1,3,7)
Show the truth table, the 4:1 MUX schematic with the inputs,
select inputs and the output.
2. For an 8:3 priority encoder:
a) Draw the schematic.
b) Write the truth table.
c) Write the Boolean expressions for each of the outputs in
terms of the inputs.
d) Draw the logic circuit for the outputs in terms of the
inputs.

3. Perform logic minimization to the following logic
functions:
(c) h(A, B, C, D, E, F) =
Sm(0,1,4,5,14,15,16,17,20,21,23,31,35,37,38,39,42,43,44,45,47,52,53,55,
56, 57, 61, 62, 63)
(e)f2(A,B,C,D,E,F) =
PM(0,2,5,7,8,10,13,15,16,18,21,23,24,26,29,31,32,34,37,42,45,46,47,
48, 50, 53, 58, 61)

Analyze following logic expression representing
a digital system,
Z = (A+C)(A'+D')(B'+C'+D)
Identify the 0-hazards and write down the logic
expression for the implementation of static free circuit. Note that
you would be requiring three additional loops in K-map

1) Implement the given logic function using a 4:1 MUX. (Ref: Lec
16, slide 5)
F(A,B,C) = Σm(0,1,3,7)
Show the truth table, the 4:1 MUX schematic with the inputs,
select inputs and the output.
2) For an 8:3 priority encoder:
a) Draw the schematic.
b) Write the truth table.
c) Write the Boolean expressions for each of the outputs in
terms of the inputs.
d) Draw the logic circuit for the outputs in terms of the
inputs.

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