ENGR 2720 Chapter 03

ENGR 2720 Chapter 03 - Chapter 3 Boolean Algebra and...

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1 Chapter 3 Boolean Algebra and Combinational Logic
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2 Chapter 3 Homework 3.2a, 3.3a, 3.5, 3.7, 3.11h, 1.13, 3.19, 3.21a&f, 3.23b, 3.35, 3.43, 3.45, 3.47, 3.63
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3 Logic Gate Network Two or more logic gates connected together. Described by truth table, logic diagram, or Boolean expression.
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4 Logic Gate Network = +
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5 Boolean Expression for Logic Gate Network Similar to finding the expression for a single gate. Inputs may be compound expressions that represent outputs from previous gates.
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6 Boolean Expression for Logic Gate Network = +
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7 Boolean Expression for Logic Gate Network + + + =
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8 Bubble-to-Bubble Convention Choose gate symbols so that outputs with bubbles connect to inputs with bubbles. Results in a cleaner notation and a clearer idea of the circuit function.
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9 Bubble-to-Bubble Convention – Step 1 Start at the output and work towards the input. Select the OR gate as the last gate for an SOP solution. Select the AND gate as the last gate for an POS solution.
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10 Bubble-to-Bubble Convention – Step 2 Choose the active level of the output if necessary. Go back to the circuits inputs to the next level of gating.
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11 Bubble-to-Bubble Convention – Step 3 Match the output of these gates to the input of the final gate. This may require converting the gate to its DeMorgan’s equivalent. Repeat Step 2 until you reach the circuits.
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12 Bubble-to-Bubble Convention – Step 3 =
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13 Bubble-to-Bubble Convention – Step 3 = Y =
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14 Order of Precedence Unless otherwise specified, in Boolean expressions AND functions are performed first, followed by ORs. To change the order of precedence, use parentheses.
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15 Order of Precedence + + + + + + +
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16 Simplification by Double Inversion When two bubbles touch, they cancel out. In Boolean expressions, bars of the same length cancel.
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17 Logic Diagrams from Boolean Expressions Use order of precedence. A bar over a group of variables is the same as having those variables in parentheses.
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18 Logic Diagrams from Boolean Expressions = + + = + +
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19 Truth Tables from Logic Diagrams or Boolean Expressions Two methods: Combine individual truth tables from each gate into a final output truth table. Develop a Boolean expression and use it to fill in the truth table.
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20 Truth Tables from Logic Diagrams or Boolean Expressions +
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21 Truth Tables from Logic Diagrams or Boolean Expressions
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22 Circuit Description Using Boolean Expressions Product term: Part of a Boolean expression where one or more true or complement variables are ANDed. Sum term: Part of a Boolean expression where one or more true or complement variables are ORed.
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Circuit Description Using Boolean Expressions Sum-of-products (SOP): A Boolean expression where several product terms are summed (ORed) together. Product-of-sum (POS):
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ENGR 2720 Chapter 03 - Chapter 3 Boolean Algebra and...

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