Q- Implement 2 variable XOR gate using NAND only in minimum number of gates. F= x XOR y = x’y+xy’ = x’y+xy’+xx’+yy’ = (x+y) (x’+y’) Now we need to implement this circuit using NAND gates F= (x+y)(xy)’ = x. (xy)’ + y. (xy)’ Take compliment F’= ( x. (xy)’ + y. (xy)’ )’ = (x. […]
Boolean Algebra
Universal Gates
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 […]
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 & […]
Example: NEGATIVE & POSITIVE LOGIC
Q- We are given a circuit as follow: Identify the above circuit as an AND or OR gate. Explain using negative and positive logic. Ans: We assume the voltage levels of +5V & 0V. So if we give both inputs as 0V then output would be 0V too. Similarly we obtain other cases as given in […]
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 […]
Negated or Bubbled gates
These are those gates which have inverted inputs to the gate as shown below: Negated AND gate is actually NOR gate while negated OR gate is NAND gate which can shown from the truth tables of Negated OR & Negated AND gate and from algebraic equations also. NEGATED AND can also be called invert-AND and NEGATED OR can be called […]
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 […]