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.
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