The full adder has 3 inputs and 2 ouputs. The first 2 inputs are the 2 bits a & b to add while the 3rd input c is the carry from the previous significant bit while the outputs are the same: sum S and the carry C. The following table shows the result of different […]
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ADDERS
Lets design the combinational circuit for binary adder. A combinational circuit that performs the addition of two bits is called Half adder while the circuit which adds 3 bits is called Full adder. Half adder: For this adder we have two inputs and two outputs. The two inputs are those 2 bits a and b which are to be […]
Combinational circuits – INTRODUCTION
The digital circuits are of 2 types: Combinational circuits: In this type of circuits, output depends only on present inputs and we don’t need memory element. Sequential circuits: In this type of circuits output depends on both present inputs and past output hence we need memory elements. We’ll first study combinational circuits. Combinational circuits: Combinational circuits consist of […]
K-maps for XOR and XNOR gates
Even variable map: For 4 variables (even), we have XOR and XNOR compliment of each other and can be represented in K-maps as follow: For XNOR gate we have 2n/2 number of min terms with output as 1 (i.e. we have even number of 0s) For XOR gate we have 2n/2 number of min terms with […]
Example: K MAPS FACTS
Q- Simplify the following Boolean function in (a) sum of products form (SOP) (b) Product of sums form (POS) F(x, y, z, w) = ∑(0, 1, 2, 5, 8, 9, 10) Ans: We mark 1s in the squares corresponding to the terms present in the function and 0s for the terms missing from the function […]
Some facts of K-map
The 1’s in the map represent min terms and 0’s represent max terms If we combine 1’s and make groups, we get simplified function. If we combine 0’s and then make groups, we get the simplified compliment function. To derive the simplified function in POS form from K map, we combine 0s and then get […]
Redundant groups
A groups of 1s or 0s whose all members are overlapped by other groups is called redundant group. We don’t consider this group while writing the simplified equations from the K-map. In the above K-map the group which is represented by the oval is a redundant group and hence while writing the equations we ignore […]
K Maps: DON’T CARES
When ever there are don’t cares present in the K-map then we have the option of including don’t care in the group to maximize the size of group and hence we get more minimized form but this is not compulsory to include each and every don’t care. So we can use don’t care to our […]
K Maps – INTRODUCTION
We want the simplest algebraic expression to represent any function so that we need minimum circuitry to implement it. The simplest algebraic expression is the one with minimum number of literals. We need to find a method to get the simplest expression. This method is called Karnaugh map method. K-map method: If we have n […]
Question 7: ANALYSIS OF NAND CIRCUIT
Q7- We implement the 3-input NAND gate circuit as follow and we are given the gate delay of d ns and 3 inputs are shown as: And give us the output of the circuit and compare it with the ideal output. Ans: Firstly we NAND of A&B is calculated and then it is inverter to get […]