The specification is shown in the grid below:
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A
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B
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C
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D
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E
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F
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G
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5
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7
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3
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0
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3
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0
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8
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You are required to design a combinational logic function with 4 inputs (P, Q, R, S) and a single output (Z). Whenever the minterm value of the inputs (PQRS) matches one of the digits in your SID the function output will be a don't care. Otherwise, the function will output a logical '1' whenever the minterm value of the inputs (PQRS) is a prime number. So that there is no confusion, for the purpose of this assignment, the numbers in the range of 4-bit minterm values that are considered prime are:
0, 1, 2, 3, 5, 7, 11, 13
Draw a truth-table to describe your function.
Plot and group the function on a Karnaugh map.
Deduce a minimal sum of products realisation for the functions making maximum use of don't care conditions.
Part B Function realisation and simulation
Draw a circuit diagram for the implementation of your function using AND, OR, NOT gates alone.
Draw a circuit diagram for the implementation of your function using only NAND gates. Include a justification using Boolean algebra for how the circuit was derived.
Draw a circuit diagram for the implementation of your function using only NOR gates. Include a justification using Boolean algebra for how the circuit was derived.
Simulate both of the circuits on Multisim to demonstrate that they comply with the specification given above. You should include a schematic of your simulation arrangement and evidence of the results. Results should be annotated or explained to detail how they show compliance. The assessor will not do this for you.