ABOUT US

Assalamualaikum and good morning everyone

today i'll introduce our team member.If you have any problem you can contact us here by clicking the name under the photo :)

                                                             Hafiz Muhamad

                                                                 Aqeelah Napis

Amni Dalilah

Liyana Roslan

Amira Nordin

This is all our group member.If you have any problem.We will try our best to help you all...:)

UNIVERSAL GATES part 2 - NOR gate

continue..

NOR GATE

Not + OR = NOR gate
                                     
Boolean Algebra = (A+B)


symbol NOR

Truth Table

Based on De Morgan's Law Gates.

      
AB





Some example NOR gate in Laws of Boolean Algebra.

equal to NAND



end..

(B031310284)
by amni dalilah

DIGITAL LOGIC (PART III)

This is the last part for this topic. Hope this part can help you to solve you problem and understand more about Digital logic,,,have funnnnnn...

4.7 LAW OF BOOLEAN ALGEBRA

• This law are use to simplify the Boolean expression.

Examples:

1. Simplify the expression below

F = (A+B) . (A+ C)

   = AA + AC + AB + BC

   = A + AC + AB + BC

   = A(1+C) + AB + BC

   = A + AB + BC

   = A(1 + B) + BC

   = A.1 + BC

   = A + BC

2. Simplify the expression using Boolean law

F = WX + XY + X'Z' + WY'Z'

   = WX + XY + X'Z' + WY'Z'X + WY'Z'X'

   = WX(1 + Y'Z') + XY + X'Z'(1 + WY')

   = WX + XY + X'Z

4.8 KARNAUGH MAP

• Provides a systematic method for simplifying Boolean expressions and produce the simplest SOP or POS expression
• This method converts the truth table information into a two-dimensional map. Its then convert’s area of 1’s on the map into groups that give the simplest expression.

Step 1: Transfer the output into Karnaugh map following the figure above

Step 2: Group the 1s output

Step 3: Convert the maps into expression

The expression is:

POS = A' + B

by nadhiah amira nordin

<B031310415>

DIGITAL LOGIC ( PART II )

hye we meet again today,,, now i want to continue the next part of digital logic
check it out..


4.4 COMBINATIONAL CIRCUITS

• Combinations of different gates in one circuit.
• The output depends only on the levels presents at input.
• Do not use any memory.
• Consists of input variables, logic gates and output variables.
• Can be represented in three ways; truth table, graphical symbols and Boolean equations.

From the figure below draw the truth table and state the Boolean equation.

Answer:

From the truth table above we can conclude that the Boolean expression is

 F = [ (A.B) + (C.D)]'

Another example:

Answer:

From the truth table, the Boolean expression;

F = (A'B) + B'A)

4.5 SUM-OF-PRODUCTS (SOP)

• Automates construction of circuit from truth table
• Identify each row of the output that has a 1 at output
• Convert into equivalent variables, AND together then OR

Example:

From the truth table below construct the SOP expression.

F = (A'B) + B'A)

Step 1: Identify rows with 1

Step 2: Put apostrophe (') over variables that is 0 in its row

Step 3: Make a sum of all product term

SOP expression = A'B + AB'

Step 4: Simplify the SOP expression

SOP = A'B + AB'

* since the expression cannot be simplify just leave the answer like that.

You don't understand???

This is another example to make you understand more..

F = A'B' + ABCD'

SOP = (A'B'C'D') + (A'B'C'D) + (A'B'CD') + (A'B'CD) + (ABC'D)

Lets continue to next subtopic..

4.6 PRODUCT-OF-SUM (POS)

• Identify each row of the output that has 0 at output
• Convert into equivalent variables, OR then AND with other OR forms.
• Usually use if more 1 produce in output function

Example:

Construct the POS expression from the truth table below.

Step 1: Identify row with 0 and put apostrophe over variables that is 1 in its row. Sum the variables as follow.

Step 2: Multiply the product term

POS = (A'+B+C) . (A'+B'+C')

Step 3: Simplify the expression

F = (A'+B+C) . (A'+B'+C')                  ---------------------- Factorize the equation

   = A'A' + A'B' + A'C' + BA' + BB' + CA' + CB' + CC'  --- Use Boolean algebra law: AA' = 0, A'A' = 0 

   = A'B' + A'C' + BA' + BC' + CA' + CB'    ----------- Factorize the same values

   = A'(B' + C' + B + C' + C) + CB'   

   = A'(1 + C') + CB'       -------- Use Boolean algebra law: A+A' = 1

   = A' + CB'

that's all for today,have fun with your study...to be continued

*if you don't understand just give me a hint then i'll upload more example for you

by nadhiah amira nordin

<B031310415>

DIGITAL LOGIC ( PART I )

 4.1 BASIC REVISION OF LOGIC GATES

What is logic gates???

Logic gates represent a true or false expression. The most common symbols used to represent a logic gates are NOT, AND, OR, NAND, NOR, XOR.

Next is i'll show you what is truth table and from the logic symbol we can draw the truth table..

4.2 TRUTH TABLE

Truth tables are used to show logic gates functions. It helps people to understand the behavior of logic gates. They show how the input(s) of logic gate relate to its output(s). When constructing a truth table, the binary values 1 and 0 are used. Every possible combination depending on number of input is produced. Basically, the number of possible combinations of 1s and 0s is 2^n where n equal to number of inputs.

4.3 DESCRIPTION OF THE SIX LOGIC GATES

NOT gate

• Produce an inversion version of an input at its output
• If the input variables is A, the inverted output fir A is known as NOT A shown as A' or A with bar over the top 
• Algebraic expression, F = A' or  F = !A

AND gate

• The output is true if both input are true.
•  A dot (.) is represents the operation of AND gate.
•  Algebraic expression, F = A.B or F = AB

OR gate

• The output is true if either one or more input true.
• A plus (+) is used to represents OR operation.
• Algebraic expression, F = A + B

NAND gate

• This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate.
• The output is true if the inputs are not both true
• Algebraic expression, F = (A.B)'

NOR gate

• This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate.
• The output is true if both inputs are not true.
• Algebraic expression, F = (A+B)'

XOR gate

• Implements an exclusive OR.
• The output is true if one, and only one, of the inputs to the gate is true.
• Algebraic expression, F = (A.B)' + (A.B)' 

that's all for today, i'll show more next time...

by nadhiah amira nordin

< B031310415 >

Number System Base

Basic Type Of Number System

A number system is a basic symbol to represent a set of quantities. There are many types of number system. Here we are only focus on the decimal, hexadecimal and binary number.

What Is A Base For Number System Type??

Today i'll show you what is about Number System Base. The system consist of :

1. Decimal
2. Hexadecimal
3. Binary Number

                                                                             Table The Type Of Number System

Decimal Number

• Base 10
• The value of the assigned weight is composed by 10 digits starting from 0 until 9.
• The positive and negative values are determined by their positions weight structure. For example:

Binary Number

• Base number 2.
• The number consists only two digit 0 and 1 only.
• The weight structure of binary number is:

• The least significant bit ( LSB ) and most significant bits ( MSB ) is depends on the size of binary number.

Hexadecimal Number

• Base of 16.
• The composed number start from 0 until F.
• The number is suitable to present in fours bit number.

It's fine to celebrate success but it is more important to heed the lessons of failure.

Bill Gates 

by Nur Aqeelah Napis

< B031310448 >

UNIVERSAL GATE part 1. NAND GATE

Universal Gate

what is universal gate?

UNIVERSAL GATE is the COMBINATION of basic gate.

NAND GATE

Not + And = NAND gate.

                                   
Boolean Algebra = (AB)

symbol NAND

Truth Table

A	B	AB	AB
0	0	0	1
0	1	0	1
1	0	0	1
1	1	1	0

Based on De Morgan's Law Logic Gates

when break the line, change the sign.

                         = 

                   

AB = A + B

The use of  NAND gate in Law Of Boolean Algebra

To be Continue----

(B031310284)

BY Amni Dalilah

NUMBER SYSTEM CONVERSION

In this post we will focused on the number system conversion of decimal,binary and hexadecimal only.There are many converting method that we can use to convert a number by using base 2,10 and 16.

2.1 Convert decimal number to binary number

To convert a decimal number into a binary number, you should carry out successive divisions by 2 and use the reminders of the successive divisions. 

Example:Convert a decimal number 40.3470₁₀ to a binary number

Firstly you should divide the number in two parts like this:

40.3470=40 and 0.347

Then,divide the number 40 with base 2 and multiply 0.3470 with base 2 as shown:

2.2 Convert binary number to decimal number

To convert a binary number into a decimal number,you should multiply with 
base 2.

Example:Convert a binary number 101112₂ to a decimal number

You should multiply the binary number with base 2 as shown:

2.3 Convert decimal number to hexadecimal number

To convert a decimal number into a hexadecimal number, you should carry out successive divisions by base 16 and use the reminders of the successive divisions. 

Example:Convert a decimal number 1850₁₀  to hexadecimal

You should divide the number with base 16 as shown:

2.4 Convert hexadecimal number to decimal number

To convert a hexadecimal number into a decimal number, you should multiply the number with base 16.

Example: Convert a hexadecimal number 5A0D₁₆  to decimal

You should multiply the number with base 16 as shown:

2.5 Convert binary number to hexadecimal number

To convert binary number into a hexadecimal number, you should multiply the number with base 2.

Example: Convert a binary number 11101001.0111₂  to hexadecimal

You should multiply the number with base 2 as shown:

2.6 Convert hexadecimal number to binary number

To convert a hexadecimal number into a binary number, you should carry out successive divisions by 2 and use the reminders of the successive divisions. 

Example:Convert a hexadecimal number E08B6₁₆ to binary number

You should divide the number with the base 2 as shown:

2’S COMPLEMENT NUMBER

What is a 2’s complement number?

Property

Two's complement representation allows the use of binary arithmetic operations on signed integers, yielding the correct 2's complement results.

Positive Numbers

Positive 2's complement numbers are represented as the simple binary.

Negative Numbers

Negative 2's complement numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero.

3.1 CALCULATION OF 2’S COMPLEMENT

To calculate the 2's complement of an integer, invert the binary equivalent of the number by changing all of the ones to zeroes and all of the zeroes to ones (also called 1's complement), and then add one.

Example:

3.2 TWO POSITIVE NUMBERS

When adding two positive numbers there is no need to do 1’s complement number and 2’s complement number.You just do like usual of binary addition as shown below.

EXAMPLE:

3.3 POSITIVE NUMBER AND SMALLER NEGATIVE NUMBER

When there is a negative number you should do 1’s complement number which is converting the ones to zeroes and zeroes to ones.Then add 1 which is 2’s complement number as shown below.

EXAMPLE:

NUR LIYANA BT ROSLAN

B031310295