NAND and NOR gates are called universal gates as any digital function can be implemented by using only NAND or NOR gate alone. Combinational and sequential both type of circuits can be implemented using NAND or NOR gate. Let’s see how we can derive all basic gates from NAND: Let’s now see that how we […]
Tag: digital electronics
Relation between XOR & X-NOR gates
As exclusive or gate gives 1 when input variables have odd number of 1’s and equivalence gate gives 1 when there are even number of zeros in input variables So when we have 2 variables then exclusive or gate gives 1 for x=0, y=1 & x=1, y=0 and it gives 0 for x=0, y=0 & […]
Tristate and Dual Inline Packaging (DIP)
Tristate gates: These are the special gates which give 3 kinds of outputs: low, high, high impedance (Z). Such gates have an extra input which is called enable input. When enable input is high, switch is closed & tristate buffer act as a normal buffer and when enable input is low output is high impedance […]
Logical Functions: XOR, XNOR
XOR: It is also called exclusive OR gate. It is an odd function. In general, it is equal to 1 if input variables have odd number of 1’s. For 2 variable it is defined as z=x’y+xy’. We don’t have muti input XOR gates because it is quiet uneconomical from hardware point of view. It is […]
Logical functions
There can be total of 2 raise to the power 2n functions possible for n binary variables. So for n=2 i.e. two variables we have total of 16 functions and we have already talked about few of those like AND, OR, NOT. So there are 13 more functions to be defined. F0=0 F1=xy F2=xy’ F3=x F4=x’y […]
Canonical Form: Relation between min and max terms
The compliment of the function expressed in terms of sum of min terms can be obtained by taking sum of missing min terms in the original functions e.g. f= ∑(4, 5, 7) = m7 + m5 + m4 Its compliment is f’ = ∑(0, 1, 2, 3, 6) = m0 + m1 + m2 + m3 + m6 The compliment […]
Boolean Equations: Different forms
Standard form: In a standard form we don’t have to compulsorily write all the literals in all the terms of an expression. e.g. f = xyz + y + x f = x’y’z’ + x’yz f= xy + x’y’ Canonical form: In a canonical form we have to compulsorily write all the literals in all the terms […]
Consensus Theorem
Consensus theorem: Given a pair of terms for which a variable appears in one term and its compliment in the other term then consensus term is formed by ANDing the original terms together leaving out the selected variable and its compliment. e.g. Find consensus term out of the two terms X.Y & X’.Z […]