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slides02 - Circuits CMSC 250 1 Find Boolean formula for q p...

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1 CMSC 250 Circuits
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2 CMSC 250 Find Boolean formula for: p, q & r are the variables. p q r output 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0
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3 CMSC 250 Find Boolean Formula For each row with output 1 obtain “mini-formula” which is 1 exactly on that row. OR together all of the mini-formulas 111, 110, and 100 all output 1 p^q^r, p^q^~r, p^~q^~r (p^q^r) (p^q^~r) (p^~q^~r)
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4 CMSC 250 Basic logic gates AND gate: OR gate: NOT gate:
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5 CMSC 250 Combining & determining I/O relationship From a circuit to a Boolean formula: p ~(q ^ r) p q r
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6 CMSC 250 Draw a circuit for: p, q & r are inputs. Simplify before building the circuit. p q r output 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0
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7 CMSC 250 Number conversions Different number system bases are used when convenient some commonly-used bases are 10 (decimal), 2 (binary), 8 (octal), 16 (hexadecimal) the base tells how many different numerals are used the base also determines the value of each place Conversions from anything to base 10 use the definition of the number system Conversions from base 10 to anything use repeated integer division
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