This document discusses various techniques for simplifying Boolean functions including K-maps, don't care conditions, and implementing Boolean functions as logic circuits. It covers:
1) Using K-maps to solve 3-variable functions and simplify sums.
2) How don't care conditions can be represented on K-maps to simplify structures.
3) Converting Boolean functions to logic diagrams using only NAND or NOR gates as universal gates. Steps are provided to convert functions to NAND and NOR gate implementations.
4) Equivalents for NOT, AND and OR gates using only NAND or NOR gates.
This presentation will help you to learn the basics required to learn the K map. This will help you to solve the questions related to K map. This presentation is actually the whole process of K map.
If you want to watch its video then go on https://www.youtube.com/watch?v=s3J0m7aZwGg
here I have explained the points mentioned in this presentation
This presentation will help you to learn the basics required to learn the K map. This will help you to solve the questions related to K map. This presentation is actually the whole process of K map.
If you want to watch its video then go on https://www.youtube.com/watch?v=s3J0m7aZwGg
here I have explained the points mentioned in this presentation
K-MAP(KARNAUGH MAP)BY THE SILENT PROGRAMMERkunal kishore
In return for this presentation please subscribe THE SILENT PROGRAMMER,,,,,,,,
where you can get different tricks to fool your pc and increase its perfomance
link:->>
https://www.youtube.com/channel/UCFxFchFfxRRxfWNCtUL7x8A
Ijcatr03051008Implementation of Matrix based Mapping Method Using Elliptic Cu...Editor IJCATR
Elliptic Curve Cryptography (ECC) gained a lot of attention in industry. The key attraction of ECC over RSA is that it
offers equal security even for smaller bit size, thus reducing the processing complexity. ECC Encryption and Decryption methods can
only perform encrypt and decrypt operations on the curve but not on the message. This paper presents a fast mapping method based on
matrix approach for ECC, which offers high security for the encrypted message. First, the alphabetic message is mapped on to the
points on an elliptic curve. Later encode those points using Elgamal encryption method with the use of a non-singular matrix. And the
encoded message can be decrypted by Elgamal decryption technique and to get back the original message, the matrix obtained from
decoding is multiplied with the inverse of non-singular matrix. The coding is done using Verilog. The design is simulated and
synthesized using FPGA.
A presentations I gave back in 2008 when I was the teaching assistant for Innovating Game Development course in Brown University.
In this presentation I talked about some common shaders used in console games such as Gaussian/motion/radial blur, depth of field, High Dynamic Range rendering, bloom, lens flare, edge glow, parallax mapping and Morgan McGuire's "Steep Parallax Mapping".
K-MAP(KARNAUGH MAP)BY THE SILENT PROGRAMMERkunal kishore
In return for this presentation please subscribe THE SILENT PROGRAMMER,,,,,,,,
where you can get different tricks to fool your pc and increase its perfomance
link:->>
https://www.youtube.com/channel/UCFxFchFfxRRxfWNCtUL7x8A
Ijcatr03051008Implementation of Matrix based Mapping Method Using Elliptic Cu...Editor IJCATR
Elliptic Curve Cryptography (ECC) gained a lot of attention in industry. The key attraction of ECC over RSA is that it
offers equal security even for smaller bit size, thus reducing the processing complexity. ECC Encryption and Decryption methods can
only perform encrypt and decrypt operations on the curve but not on the message. This paper presents a fast mapping method based on
matrix approach for ECC, which offers high security for the encrypted message. First, the alphabetic message is mapped on to the
points on an elliptic curve. Later encode those points using Elgamal encryption method with the use of a non-singular matrix. And the
encoded message can be decrypted by Elgamal decryption technique and to get back the original message, the matrix obtained from
decoding is multiplied with the inverse of non-singular matrix. The coding is done using Verilog. The design is simulated and
synthesized using FPGA.
A presentations I gave back in 2008 when I was the teaching assistant for Innovating Game Development course in Brown University.
In this presentation I talked about some common shaders used in console games such as Gaussian/motion/radial blur, depth of field, High Dynamic Range rendering, bloom, lens flare, edge glow, parallax mapping and Morgan McGuire's "Steep Parallax Mapping".
I am Anne L. I am an Algorithms Design Homework Expert at programminghomeworkhelp.com. I hold a Ph.D. in Programming, Auburn University, USA. I have been helping students with their homework for the past 8 years. I solve homework related to Algorithms Design.
Visit programminghomeworkhelp.com or email support@programminghomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with the Algorithm Design Homework.
I am Justin M. I am an Algorithm Design Exam Expert at programmingexamhelp.com. I hold a Bachelor of software engineering from, the University of Massachusetts Amherst, United States. I have been helping students with their exams for the past 9 years. You can hire me to take your exam in Algorithm Design.
Visit programmingexamhelp.com or email support@programmingexamhelp.com. You can also call on +1 678 648 4277 for any assistance with the Algorithm Design Exam.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
Ec2203 digital electronics questions anna university by www.annaunivedu.organnaunivedu
EC2203 Digital Electronics Anna University Important Questions for 3rd Semester ECE , EC2203 Digital Electronics Important Questions, 3rd Sem Question papers,
http://www.annaunivedu.org/digital-electronics-ec-2203-previous-year-question-paper-for-3rd-sem-ece-anna-univ-question/
Implementation of Low-Complexity Redundant Multiplier Architecture for Finite...ijcisjournal
In the present work, a low-complexity Digit-Serial/parallel Multiplier over Finite Field is proposed. It is
employed in applications like cryptography for data encryption and decryptionto deal with discrete
mathematical andarithmetic structures. The proposedmultiplier utilizes a redundant representation because
of their free squaring and modular reduction. The proposed 10-bit multiplier is simulated and synthesized
using Xilinx VerilogHDL. It is evident from the simulation results that the multiplier has significantly low
area and power when compared to the previous structures using the same representation.
7. Solving Three variable function with K – Map
Z = f(A,B,C) = A̅B̅C̅ + AB + ABC + AC
= A̅B̅C̅ + ABC + ABC +ABC + ABC + ABC
Sol. is F = B + AC + AC
8. Productionof Sums Simplification
e.g. F(A ,B ,C ,D) = Σ(0,1,2,5,8,9,10)
Solution:Creating a four variable K-map for above function , we have
In this K–map combination of 0s are made to get solution for complement of F.
so, F’ = AB + CD + BD’
Now F = (F’)’ = (AB + CD + BD’)’
= (A’ + B’) . (C’ + D’) . (B’ + D)
Which is required product of sum simplification.
9. Don’t Care Conditions
Till now we have discussed function in which the combination of variable are either 0 or 1 and
accordingly map created. The combination usually taken from the truth table for which the
value is evaluated to 1. value for all other combination is assumed to be 0. however this not
always true. There may be some certain application where for certain combination, there are
no output value e.g. in some digital circuit, if we have to take six input combination, we have to
take 3 input variables leading to total of 2³ i.e. 8 combinations. So out of these 8
combinations 2 will be unused. So we don’t care about these value. These don’t care condition
can be used in map to have simpler structure. Don’t Care combination on a K-Map are marked
with ‘X’ to distinguish them from value 0 or 1. Following point should be taken while making
combination with don’t care squares-
1. If a combination with equal no. of squares is possible with higher no. of 1’s then that
combination is given preference over the combination that contain more no. ‘X’ squares.
2. It is not necessary that all squares containing ‘X’ take part in making combinations.
3. Each combination containing X must have atleast one 1.
10. Example : Simplify F (w, x, y, z) = Σ(1, 3, 7, 11, 15)
D(w, x, y, z) = Σ(0, 2, 5)
Solution :Creatinga four variable K-map –
Finding common value in combination, the solution will be
F = wz + yz
11. IMPLEMENTING BOOLEAN EXPRESSION AS DIGITAL CIRCUITS
For any Boolean function you can design an electronicand vice versa. Since Boolean function only
requirethe AND , OR, and NOT boolean operators,which will be used to representAND (.), binary
OR (+) and compliment (‘) respectivelyin Boolean algebraicfunctions.
Using these gate we can design logical diagram for any of the Boolean function.
12.
13. Some other logic gates which are very commonly used in designing logic circuit are given as below :
14. NAND and NOR gates as UniversalGates
One interestingfact is that you only need a single gate type to implement any electronic circuit. There
are two gates which serve this purpose. There are NAND gate and NOR gate that is why these gate
also known as universalgates.
Converting A Function Into Logic Diagram With Only NAND Gates : Following step s have
performedfor doing this:
1. Get the simplified form of function in sum of product form.
2. Draw a NAND gate for each productterm of the function that has at least two variable . Thesewill
become firstlevel gate.
3.Draw a single NAND gate in second level that have input as output from first level gate.
4. Termwith single variablecan be complementedand applied as input to second level NAND gate.
Now using same rule we will convert AND, OR And NOT into NAND gate circuits.Remember function
for these gates are already in simplified form.
16. E.g. F = (AB+CD) . BC
Let us draw logical diagram for this
17.
18. Implementing Logic Circuit Using NOR Gate Only
For two level circuit, following step are performed :
1. Simplify function in product of sum form.
2. Apply same step as two level NAND implementation except term for firs level NOR gates are sum
terms.
3. Similarly,a single variableterm will need one input NOR gate.
NOT, OR & AND gates equivalentto NOR gate: