ABCD out ABCD out 1000 1 1 0 0 1 1 1 0 1 0 1 101 10 00001 00011 00101 00111 D1 0 0 1 01011 01101 0 1 1 1 1 11000 11011 11100 1 1 1 1 1
For the following truth table and expression please do the following;
A'B'C'D' + AB'C' + AB'C'D' + ABD + A'B'CD' + BC'D + A'
A. Draw a Karnaugh map for the truth table below 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. Using the Karnaugh map from part (a), write down the minimal sum-of-products expression for the original boolean expression.
c. 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.
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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