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 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

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