LOGIC GATES In this post we are going to learn about all the logic gates, their symbols, truth table and the logic equations. The different logic gates that will be covered are: 1. BUFFER 2. NOT 3. OR 4. AND 5. NAND 6. NOR 7. XOR 8. XNOR Binary Values: When only two possible states are to

# Boolean Postulates and Theorem

BOOLEAN POSTULATES and THEOREM Boolean algebra was introduced by George Boole in 1854. Boolean algebra is used to perform binary and logical operations and differs in this respect from the ordinary algebra. Postulates of Boolean Algebra 1. Identity Law : A + 0 = A A.1 = A 2. Commutative Law: (A+B) = (B+A) A.B = B.A 3. Associative Law: A + (B + C) = (A + B) + C A.(B.C) = (A.B).C 4. Distributive Law: A . (B + C) = A.B + A.C A + (B.C) = (A + B). (A + C) 5. Complement Law: A+A’ = 1 A.A’ = 0 Boolean Algebra Theorems 1. Duality Theorem: It states that we can derive a Boolean relation from another Boolean relation by just : i. Changing the ‘.’ With a ‘+’ and ‘+’ with

# Number System Representation

Data representation 1. Unsigned Magnitude Representation 2. Signed Magnitude 3. 1’s Complement 4. 2’s Complement 1. Unsigned Number Representation In this representation all the bits represent only the magnitude of the number without consideration to the sign of the number. Example: D7 D6 D5 D4 D3 D2 D1 D0 Value Minimum Value 0 0 0 0 0 0 0 0 0 Maximum Value 1 1 1 1 1 1 1 1 2N-1 =255 The range of the numbers that can be represented in this representation is 0 to 2N-1 For 1 4-bit number the range will be = 0 to 24-1 = 0 to 15 For an 8-bit number the range will be = 0 to 28-1 = 0 to 255 · Note: We cannot represent signed number in this representation. Signed and Magnitude number Representation: We have only +ve or the –ve numbers. Two states can be represented by only a single bit. For convenience and also as standard

# 1. Number System

What is a Number? A number is a mathematical value used for counting or measuring or labelling objects. In number system these numbers are used as digits. Number Systems A number system is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figure. The value of any digit in a number can be determined by: The digit Its position in the number The base of the number system Number System Chart There are various types of number systems in mathematics. The four most common number system types are: Decimal number system (Base- 10) Binary number system (Base- 2)

# Number System

Number: A number is a mathematical value used for counting or measuring or labelling objects. In number system these numbers are used as digits. Number Systems A number system is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figure. The value of any digit in a number can be determined by: The digit Its position in the number The base of the number system Number System Chart There are various types of number systems in mathematics. The four most common number system types are: Decimal number system (Base- 10) Binary number system (Base- 2) Octal number