About logic diagram, boolean algebra, computer organization
Draw the logic diagram for function F as a 2‐level AND‐OR circuit.
Background
F(a,b,c) --> F output 1 if abc is interpreted as 3-bit unsigned integer is a prime number. Output is 0 for other numbers.
The Simplified SOP Expression of F = a'b + ac
F (a, b, c) = m (2, 3, 5, 7)
Note:
i) complemented inputs (a', b', c') are not available;
ii) Use a fan‐in of 2 only. (i.e. AND / OR gate takes only 2 inputs).
Label the final output and all intermediate outputs. Use
product/sum term, e.g. a.b.c instead of minterm/maxterm notation,
e.g. m7.
Given that we need to design a 2 level AND-OR circuit
of F where
F(a,b,c)=m(2,3,5,7)
SOP expression
F=a'b+ac
F is 1 when abc which is a 3-bit unsigned integer is prime
Also fan-in 2 logic gates are available
The truth table of F is
a | b | c | F |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 |
The circuit diagram is
Note:-NOT gates does not count towards depth of circuit
About logic diagram, boolean algebra, computer organization Draw the logic diagram for function F as a...
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