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Published byJoanna Lester Modified over 6 years ago

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Logic gates & Boolean Algebra

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Introduction Certain components (called logic elements) of the computer combine electric pulses using a set of rules. Electric pulses are called digital signal. Digital signals have 2 voltage levels: HIGH (binary 1) and LOW (binary 0). Binary 1 = true or on. Binary 0 = false or off.

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Primary logic gates OR gate –Output is 1 if any of its input is 1 AND gate –Output is 1 if all of its input is 1 NOT gate –Output is the reverse of the input. Has one input and one output. ABY 000 011 101 111 Truth Table ABY 000 010 100 111 AY 01 10 Y = A + B Y = A. B Y = Ā

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Secondary logic gates NOR gate –Output is 1 if all of its input is 0 NAND gate –Output is 0 if all of its input is 1 EXOR gate –Output is 1 if the inputs are different. ABY 001 010 100 110 Truth Table ABY 001 011 101 110 Y = A + B Y = A. B Y = A B ABY 000 011 101 110

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Boolean algebra & logic simplification Logic circuits can be simplified by Boolean algebra. Boolean theorems are used to simplify circuits. Basic theorems: OR NOT AND A + 0 = A A + 1 = 1 A + A = A A + Ā = 1 A. 0 = 0 A. 1 = A A. A = A A. Ā = 0 A = A

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Other theorems: A + B = B + A A. B = B. A A + (B + C) = (A + B) + C A + B. C = (A + B) (A + C) A. (B + C) = A. B + A. C A + A. B = A Operator Precedence –( ), NOT, AND, OR –Example, A + B. C = A + (B. C) –Example, Ā. Ī = (Ā). (Ī) DeMorgan’s theorem –A + B = A. BFor 3 variables:- A + B + C = A. B. C – A. B = A + BFor 3 variables:- A. B. C = A + B + C ABA + BA. BA + BABA. BA + BA. B 0000111111 0110010011 1010001011 1111000000

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