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The Boolean function is given as: F=(X+Y)Z′ To design the circuit: The inputs X and Y are first OR-ed together, so an OR gate is used to perform X+Y. The input Z is inverted using a NOT gate, so we get Z′. Finally, the output of the OR gate and the NOT gate are AND-ed … Read more
Let’s simplify the given Boolean function: F=X′Y+XY′+X First, group terms to factorize: F=(X′Y+XY′)+XY The term X′Y+XY′ is the Boolean expression for XOR, so we have: F=(X⊕Y)+XY Now, we simplify further by noting that the expression (X⊕Y)+XY is just an OR operation between the XOR of X and Y and the AND of X and Y. This … Read more
The XOR (Exclusive OR) gate works by outputting true (1) when the number of true inputs is odd. For a 2-input XOR gate, the output is 1 only if the inputs are different, and 0 if they are the same. The Boolean expression for a 2-input XOR gate is: A⊕B=A′B+AB′ This expression means that the … Read more
Boolean algebra simplifies logic circuits by reducing the number of gates and variables needed. Using laws like idempotent, absorption, distribution, and De Morgan’s theorem, one can manipulate Boolean expressions to minimize the complexity of the logic circuit. This simplification often leads to faster, less costly, and more efficient circuit designs. Related Questions: What is a … Read more
The NAND gate is considered a universal gate because it can be used to implement any Boolean function or other logic gates (AND, OR, NOT, etc.) by combining multiple NAND gates in different configurations. Specifically, a NAND gate can be used to form NOT gates, AND gates, and OR gates, making it versatile for all … Read more
De Morgan’s Theorems are important for simplifying and transforming Boolean expressions involving negations. They state: The complement of a product of variables is equal to the sum of the complements: (AB)′=A′+B′ The complement of a sum of variables is equal to the product of the complements: (A+B)′=A′B′ These laws allow for the conversion between AND … Read more
The complement of a Boolean function is the inverse of the function, where all the logic values are inverted. If the function is represented as F, then the complement is denoted as F’, which is obtained by changing all 1s to 0s and vice versa. The complement operation can be calculated using De Morgan’s laws … Read more
The XOR (Exclusive OR) gate is a digital logic gate that outputs true (1) when the number of true inputs is odd. For a 2-input XOR gate, it outputs 1 when one of the inputs is 1 and the other is 0, and outputs 0 when both inputs are the same (either both 0 or … Read more
F = X’Y’Z + X’YZ:This function requires three variables X, Y, and Z and two AND gates (for X’Y’Z and X’YZ) and an OR gate to combine the results. F = X + YZ:This function uses an OR gate to combine the variable X and the output of an AND gate that combines Y and … Read more
For F = X’Y’Z + YZ + XY’Z, simplifying with a K-map gives:F=Z+Y′ZF = Z + Y’ZF=Z+Y′Z For F = XZ + Y’Z + XYZ, simplifying with a K-map gives:F=ZF = ZF=Z For F = YZ + Y’Z + Z’YZ + XY’Z, simplifying with a K-map gives:F=ZF = ZF=Z For F = X’Y + X’Y’, … Read more