For the following truth table and expression please do the following; A′B′C′D′+AB′C′+AB′CD′+ABD+A′B′CD′+BC′D+A A. Draw a Karnaugh map for the truth table above Make sure to circle the map accordingly to indicate the product terms needed to derive a minimal sum-of-products. Each circled block must be a maximal (that is, as large as possible without containing a 0 or being a non-power-of-two) rectangle of 1s whose width and height are powers of two. These rectangles may wrap around the edges of the diagram and may overlap. b. Construct a new circuit that outputs 1 precisely when a 3-bit input ?, interpreted as a 3-bit unsigned integer, is a prime number and outputs 0 otherwise. Call the three input lines A2,A1,A0, and consider A3 as the most significant bit and A0 as the least significant bit. Draw a Karnaugh map for this circuit. c. Using the Karnaugh map from part (b), write down the minimal sum-of-products expression to determine if a 3-bit unsigned integer is prime.
For the following truth table and expression please do the following;
A′B′C′D′+AB′C′+AB′CD′+ABD+A′B′CD′+BC′D+A
A. Draw a Karnaugh map for the truth table above Make sure to circle the map accordingly to indicate the product terms needed to derive a minimal sum-of-products. Each circled block must be a maximal (that is, as large as possible without containing a 0 or being a non-power-of-two) rectangle of 1s whose width and height are powers of two. These rectangles may wrap around the edges of the diagram and may overlap.
b. Construct a new circuit that outputs 1 precisely when a 3-bit input ?, interpreted as a 3-bit unsigned integer, is a prime number and outputs 0 otherwise. Call the three input lines A2,A1,A0, and consider A3 as the most significant bit and A0 as the least significant bit. Draw a Karnaugh map for this circuit.
c. Using the Karnaugh map from part (b), write down the minimal sum-of-products expression to determine if a 3-bit unsigned integer is prime.
Karnaugh Map, often referred to as a K-map, is a graphical representation and simplification tool used in digital logic design to analyze and minimize Boolean functions. It is particularly useful for simplifying logical expressions, optimizing digital circuits, and reducing the number of logic gates required for a given logic function.
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