Skip to main content

INTEGRATED CIRCUITS WITH A SOFTWARICAL TWIST

LOGICAL DESIGN OF FUNCTION OF INTEGRATED CIRCUITS
john green,редстоун,провод,индикатор,экран,дисплей,логика,лазер,cad,кад,интегральные схемы,project red,red power,схемы,гейт,1.7.10,подробно,руководство,учебник,туториал,гайд,обзор,по-русски,на русском,мод,майнкрафт,туннель,логический,minecraft ics,electronics & communications engineering,gates,logic


A binary variable or called as two value variables can take the value of 0 or 1.  A Boolean functions or named as two variable function is an expression formed with binary variables, the two binary operators OR and AND, the unary operator NOT, parenthesis, and equal sign.  For a given value of the variables to made it as good and thorough, the function can be either 0 or 1.  Consider, for example, the Boolean function:

                                                 F1 = xyz’

The function as shown above F1 is equal to 1 if x = 1 and y = 1 and z’ =  1; otherwise F1 = 0.  The above is an example of a Boolean functions represented as an algebraic expression.  A Boolean function may be represented in a truth table.  To represent a function of a truth table we need a list of 2^n combination of 1s and 0s of the n binary variables and a column showing the combinations for a function equal to 0 or 1.
john green,редстоун,провод,индикатор,экран,дисплей,логика,лазер,cad,кад,интегральные схемы,project red,red power,схемы,гейт,1.7.10,подробно,руководство,учебник,туториал,гайд,обзор,по-русски,на русском,мод,майнкрафт,туннель,логический,minecraft ics,electronics & communications engineering,gates,logic


As shown in Table below, there are eight possible distinct combination for assigning bits to three variables.  The column labeled F1 when x =1, y = 1, and z=0.  It is equal to zero otherwise.  Consider the function
  F2 = x + y’z

F2 = 1 if x = 1 or if y = 0, while z = 1.  In another table , x = 1 in the last four rows and yz = 01 in rows 001 and 101.  The later combination applies also for x = 1.  Therefore there are five combination that make F2 = 1. As a third example, consider the function:

F3 = x’y’z’ + x’yz + xy’

This is shown in table below with four 1’s four 0’s.  F4 is same as F3 and is considered below

Truth tables for F1 = xyz’,  F2 = x + y’z ,  F3 = x’y’z + x’yz + xy’
and F4= xy’ + x’z

X
Y
Z
F1
F2
F3
F4
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0

Any Boolean function or a Boolean equation can be represented in a truth table or any mathematical drawing .  The numbers of rows in the table is 2n where n is the number of binary variables  in the function.  The 1’s and 0’s combination for each row is easily obtained from the binary numbers by counting 0 to    2n – 1.  For each row of the table, there is a value for the function equal to either 1 or 0.  The question now arises, is an algebraic expression of a Boolean function is unique ? In other words, is it possible to find two algebraic expression that specify the same function?  The answer to this question is yes.  As a matter of fact, the manipulation of Boolean algebra is applied mostly to the problem of finding simpler expression for the same function.

Consider for example the functions:
                                F4 = x y’ + x’ z
From table above, we find that F4 is same as F3  since both have identical 1’s  and 0’s for each combination of values of the three binary variables.  In general or in simply terms, two functions of n binary variables are said to be equal if they have the same value for all possible 2n combinations of the n variables.

Comments

Post a Comment

Popular posts from this blog

EXPANSION SLOTS IN MOTHERBOARD

EXPANSION SLOTS IN MOTHERBOARD  Friends today i am going to share my knowledge and understanding of the expansion slots. So lets begin with our topic. Expansion slots are used to provide additional properties for carrying the computation task such as additional video, audio and sound, advanced graphics and Ethernet.   So lets begin with our knowledge hunting. I will start by AGP expansion slots. AGP AGP stands for ACCELARATED GRAPHICS PORT.  AGP was introduced with high speed 3D graphics display in 1996.  It is used for older graphics card types which is discontinued by PCI EX16 graphics port in 2005.   These were kernel version of AGP most of the brand in 1.5 volt DC.  AGP 1x channel and 66MHZ clock speed resulting a data table of 266 MBPS.   AGP 2x, 4x ,8x specification multiply MHZ clock to produce increase throughput. AGP 8x produces effective clock frequency of 533 MHZ resulting a throughput of 2 GBPS (2133MHZ) resulting a throughput of over a 32 bit channel. PCI PCI  stands for P

PROCESSOR AND HYPER THREADING A SHORT SUMMARY

PROCESSOR AND HYPERTHREADING Friends in the last post i tried to say something about computer science and mathematics relationship.   Now i am going to say something about processor and hyperthreading.   So let’s get started. The Physical Component By Which A Computer Is Made Which We Can See, Touch And Feel Is Called Computer Hardware Example Ram, Motherboard. ·          INPUT DEVICE   : These hardware are used to input any data, instruction on command insidea computer device.   example keyboard mo9use scanner microphone, webcam etc ·          OUTPUT DEVICE :   these hardware are used to get any output from a computer system.   example: monitor, printer, speaker. ·          CENTRAL PROCESSIG UNIT (CPU) : This Device Proceses All Instruction Given By A User, And It Also Other Haqrdwqaar Peripherals Example   :Microprocessor ·          MOTHERBOARD: It is the main electric circuit board which is made by a pcb(printed circuit board).   It hods all hardware componen

CODES OF LANGUAGE IN COMPUTER SYSTEM. WHAT ARE THE OTHER CODES WHICH ARE USED IN COMPUTER SYSTEM?

  CODES OF LANGUAGE IN COMPUTER SYSTEM.   WHAT ARE THE OTHER CODES WHICH ARE USED IN COMPUTER SYSTEM?   There are many codes in computer system which may remain unnoticed by many computer geeks and nerds.   I also first didn’t see it but I am going to share it because these are important codes and used by many computer hardware developers, vendors and computer software developers.    They are mostly understood by ELECTRONICS AND ELECTRICAL ENGINEERING geeks or nerds.   They are as under : ·         ERROR DETECTION CODES ·         ALPHANUMERIC CODES ·          REFTLECTED CODES First we will discuss something about ERROR DETECTION CODES.                                                                                                              ERROR DETECTION CODES:   Binary information , be it pulse modulated signals or digital computer input or output, may be transmitted though some form of communication medium or electrical wires or radio waves.   Any external noi