What is XOR Boolean expression?
The Boolean expression for XOR gate cannot determined directly like AND, OR gates. As it is a Hybrid gate, the Boolean expression of output of XOR gate is given by a combining of Multiplication, Addition and inverting of inputs.
What is the truth table of 4 to 1 multiplexer?
The truth table of a 4-to-1 multiplexer is shown below in which four input combinations 00, 10, 01 and 11 on the select lines respectively switches the inputs D0, D2, D1 and D3 to the output. That means when S0=0 and S1 =0, the output at Y is D0, similarly Y is D1 if the select inputs S0=0 and S1= 1 and so on.
How do you solve a Boolean function with a multiplexer?
How to solve?
- The first step is to select the multiplexer.
- Connect the inputs, that correspond to the given minterms to logic 1.
- Connect all the other inputs to the ground(logic 0).
- Connect the input variables(P, Q, R) as the selection lines.
How do you find the XOR of two numbers?
To find the XOR of two numbers, follow these instructions:
- Convert the numbers into the binary representation.
- Compare the corresponding bits of the two numbers.
- If only one of the input bits is true (1), the output is true (1). Otherwise, the output is false (0).
What is the truth table for XOR gate?
Truth Table: The output of an XOR gate is high (1) only when exactly one of its inputs is high (1). If both of an XOR gate’s inputs are low (0), or if both of its inputs are high (1), then the output of the XOR gate is low.
How many 2 1 muxes are required to implement an XOR function?
Implementation of NAND, NOR, XOR and XNOR gates requires two 2:1 Mux. First multiplexer will act as NOT gate which will provide complemented input to the second multiplexer. Three(3) 2 : 1 MUX are required to implement 4 : 1 MUX.
How do you make an XOR gate with NAND gates?
An XOR gate is made by connecting four NAND gates as shown below….XOR.
| Desired XOR Gate | NAND Construction |
|---|---|
| Q = A XOR B | = [ A NAND ( A NAND B ) ] NAND [ B NAND ( A NAND B ) ] |
| Truth Table Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 0 |
How do you write a mux equation?
We can confirm this in the following Boolean expression.
- Q = A.I0.I1 + A.I0.I1 + A.I0.I1 + A.I0.I1
- Q = A.I1 + A.I0
- The Boolean expression for this 4-to-1 Multiplexer above with inputs A to D and data select lines a, b is given as:
- Q = abA + abB + abC + abD.
How do you implement a Boolean function?
Any Boolean function can be implemented using only AND and INVERT gates since the OR function can be generated by a combination of these two gates, as shown in Figure 2.20(a). It follows that these two gates can implement any arbitrary Boolean function and they are said to form a complete set.
What is Boolean expression for XOR gate for input A and B?
An XOR gate is also called exclusive OR gate or EXOR. In a two-input XOR gate, the output is high or true when two inputs are different. In Boolean expression, the term XOR is represented by the symbol (⊕) and the Boolean expression is represented as Y = A ⊕ B. It is read as “A xor B”.
What is the Boolean expression for XNOR gate?
XNOR: the Boolean expression for the XNOR gate is: \(Y = A \cdot B + \bar A\bar B\).
How many and or and XOR gates are required for the configuration of full adder?
Explanation: There are 2 AND, 1 OR and 2 EXOR gates required for the configuration of full adder, provided using half adder. Otherwise, configuration of full adder would require 3 AND, 2 OR and 2 EXOR.
What is the minimum number of 4×1 Multiplexers required to implement a full adder?
Full Adder using 4 to 1 Multiplexer: A 4 to 1 line multiplexer has 4 inputs and 1 output line.In our experiment,we use IC 74153(Multiplexer) and IC 7404(NOT gate) for implementing the full adder.
How many not gates are required for the construction of a 4 to 1 multiplexer?
two NOT gates
Explanation: There are two NOT gates required for the construction of 4-to-1 multiplexer. x0, x1, x2 and x3 are the inputs and C1 and C0 are the select lines and M is the output.
How many 4 1 muxes are needed to build a 128 1 mux?
you need 43 (4×1) muxes to implement a (128×1) mux.
What is the Boolean expression of a 4 input NAND gate?
Logic NAND Gate Equivalence The Boolean expression for a logic NAND gate is denoted by a single dot or full stop symbol, ( . ) with a line or Overline, ( ‾‾ ) over the expression to signify the NOT or logical negation of the NAND gate giving us the Boolean expression of: A.B = Q.
How do you solve a multiplexer?
Procedure:
- Firstly truth table is constructed for the given multiplexer.
- Select lines in multiplexer are considered as input for the truth table.
- Output in truth table can be four forms i.e. ( 0, 1, Q, Q’).
- Now with the help of truth table we find the extended expression.
Which decoder will be used to implement 3 variable Boolean expressions?
From the above Boolean expressions, the implementation of 3 to 8 decoder circuit can be done with the help of three NOT gates & 8-three input AND gates.
How many possible 4 variable Boolean function exist?
As the number of variables increases, the number of Boolean functions that can be formed increases rapidly. For three Boolean variables there are 28 = 256 possible Boolean functions, for four variables there are 216 = 65 536 possible Boolean functions and for n variables there are 2(2n) possible Boolean functions.
How do you find XOR from 1 to N?
1- Initialize the result as 0. 1- Traverse all numbers from 1 to n….Method 2 (Efficient method) :
- Find the remainder of n by moduling it with 4.
- If rem = 0, then XOR will be same as n.
- If rem = 1, then XOR will be 1.
- If rem = 2, then XOR will be n+1.
- If rem = 3 ,then XOR will be 0.
How do you solve a Boolean expression with multiplexer?
Implement the boolean expression F (A, B, C) = ∑ m (0, 1, 3, 5, 7) using a multiplexer. Similar to the above problem, there are 3 variables and hence 8 : 1 multiplier is used to solve the expression.
What is 4 to 1 multiplexer?
One of these data inputs will be connected to the output with the select lines. Since there are ‘n’ selection lines, there will be about 2 n combinations of “1” and “0”. 4 to 1 Multiplexer is also known as 4 to 1 MUX circuit. In this tutorial, we are going to steady about behavior of 4 to 1 multiplexer.
What is the output of the multiplexer when S 0 =0?
According to the truth table, the output of the multiplexer fully depends on selection lines (binary data , 00,01,10 & 11) and one input would be selected from all the input data lines as the output. When S 0 =0 and S 1 =0 , then A 0 would be the output.
How to implement F (A B C C D) using 8 1 multiplexer?
Implement F (A, B, C, D) = ∑ m (0, 1, 5, 6, 8, 10, 12, 15) using 8 : 1 multiplexer. In the given boolean expression, there are 4 variables. We should use 2 4 : 1 = 16 : 1 multiplexer. But as per the question, it is to be implemented with 8 : 1 mux. For 8 : 1 multiplexer, there should be 3 selection lines.