FreeNotes
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
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
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
F = X’Y’Z + YZ + XY’Z X Y Z X’ Y’ F = X’Y’Z + YZ + XY’Z 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 … Read more
NAND Gate: A NAND gate can be created by first using an AND gate to perform the logical AND operation on two inputs, and then applying a NOT gate to the output of the AND gate. The expression for a NAND gate is:F=A⋅B‾F = \overline{A \cdot B}F=A⋅B, which means the output is the negation … Read more
AND Gate: Symbol is a flat-ended shape with two inputs and one output. Function: The output is 1 only if both inputs are 1. (A AND B = 1 if A = 1 and B = 1) OR Gate: Symbol is a curved shape with two inputs and one output. Function: The output is 1 … Read more