ICDL-ASSIGNMENT

1. ICDL-ASSIGNMENT • BOOLEAN ALGEBRA • LOGIC GATES & CIRCUITS Presented By: MAC Fathima Farvin KM/Shams Central College Maruthamunai. Trained By: IDM Computer Systems.

2. ENGAGEMENTBOOLEAN ALGEBRA • AND,OR,NOT gates operations are explained using the Boolean Algebra here. • Boolean algebra uses two value either 1 or 0. • Here the results will be true [1] or false[0] AND Operation • The AND gate has two or more inputs. The output from the AND gate is 1 if and only if all the inputs are 1,otherwise the output from the gate is 0. OR OPERATION • The OR gate has two or more inputs. The output from the OR gate is 1 if any of the inputs is 1, the output from the gate is 0 if and only if all inputs are 0. NOT OPERATION • If the input will be 0,out put value 1 ,if input value1 out put also 0. Inversion • Inversions of AND ,OR ,XOR gates are NAND ,NOR, XNOR consequently.

3. EXPLANATION AND ELOBARATION • Boolean arithmetic exploration by adding and multiplying numbers. OR Gate AND Gate 0 + 0 = 0 0 + 1 =1 1 + 0 = 1 1 + 1 = 1 0  0 = 0 0  1 = 0 1  0 = 0 1  1 = 1

4. This following diagrams shows how axioms are derivedTHE FOLLOWING DIAGRAM SHOWS HOW AXIOMS ARE DERIVED.I

5. x+x=x, axiom is derived from the four diagrams below

6. Axiom 0.X=0, is derived from the two diagrams below

7. Axiom 1.X=X, derived from the diagrams below .

8. In written form,the compliment of “ A” is denoted as “A-not” or “A-bar”. Sometimes a “prime” symbolis used to represent complementation. COMPLEMENTATION • This notation “bar" above variables is used to denote complementation as shown below

9. Multivariable Theorems The theorems presented below involve more than one variable: • x + y = y + x (commutative law) • x * y = y * x (commutative law) • x+ (y+z) = (x+y) +z = x+y+z (associative law) • x (yz) = (xy) z = xyz (associative law) • A). x (y+z) = xy + xz • b).(w+x)(y+z) = wy + xy + wz + xz • x + xy = x • x + x'y = x + y

10. De Morgans theorems • It is use ful in simplifying expression in which a product or sum of variable is inverted. The two theorems are: A) . (x+y)' = x' * y' B) . (x*y)' = x' + y' Theorem (A) says that when the OR sum of two variables is inverted This is the same as inverting each variable individually and then AND in these inverted variables. Therem (B) says that when the AND product of two variables is inverted This is the same as inverting each variable individually and then OR in them.

11. IMPLICATION OF DeMorgans Theorem • a): (x+y)' = x' * y'

12. For (B): (x*y) = x + y

13. Following is an example of a circuit using Boolean expression

14. Whenever an inverter is present what is out put expression

15. EVALUATION 1) Boolean Logic uses _________ to determine how bits are compared and simulate ________ . A) Operators, Gates B) Buffers, AND C) Truth Tables, Off D) NOR, NAND 2) The _______ operation says if and only if all inputs are on, the output will be on. The output will be off if any of the inputs are off. A) OR B) NAND C) NOR AND • 3) The ______ operation says if any input is on then the output will be on. • NOT B) OR C) NOR D) XOR 33 )

16. 4) If all of the inputs are on, the output will be off. This is called _______. A) NAND B) NOR C) Truth Tables D) On 5) This operation says that if any input is on, the output will be off. Which operation is this? A) Boolean Logic B) XOR C) NOR D) AND 6) ________ says that if the inputs are different then the output will be on. A) Gates B) Low C) NXOR D) XOR

17. EVALUATION FOR MULTIVARIABLE THEORAMS • What function are implemented by the following circuits shown below?