9618 · 15.2
Boolean Algebra and Logic Circuits flashcards
Revision flashcards for Cambridge 9618 Boolean Algebra and Logic Circuits (syllabus 15.2). Flip, recall, then mark a real past-paper question.
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De Morgan's Law (First Law)
The negation of a conjunction is the disjunction of the negations. Algebraically: $\overline{A \cdot B} = \overline{A} + \overline{B}$. In logic gates, a NAND gate is equivalent to an OR gate with inverted inputs.
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De Morgan's Law (Second Law)
The negation of a disjunction is the conjunction of the negations. Algebraically: $\overline{A + B} = \overline{A} \cdot \overline{B}$. In logic gates, a NOR gate is equivalent to an AND gate with inverted inputs.
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Distributive Law
AND distributes over OR: $A \cdot (B + C) = A \cdot B + A \cdot C$. OR distributes over AND: $A + (B \cdot C) = (A + B) \cdot (A + C)$.
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Absorption Law
A set of laws that simplify expressions where a variable is combined with a term containing that same variable. Key forms: $A + (A \cdot B) = A$ and $A \cdot (A + B) = A$.
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Karnaugh Map (K-map)
A graphical method used to simplify Boolean algebra expressions. It's a grid where cells represent minterms, and adjacent cells differ by only one variable, allowing for visual grouping to find a minimal sum-of-products form.
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Sum-of-Products (SOP)
A standard form for a Boolean expression where several product terms (AND operations) are summed together (OR operation). For example: $A\overline{B} + \overline{A}C$.
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Combinational Logic Circuit
A type of digital circuit whose output is solely determined by its current input values. It has no memory. Examples include adders, decoders, and multiplexers.
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Sequential Logic Circuit
A type of digital circuit whose output depends not only on the current inputs but also on the previous sequence of inputs, due to internal memory elements. Examples include flip-flops and counters.
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Half Adder
A combinational circuit that adds two single binary digits (A and B) and produces two outputs: Sum (S) and Carry (C). S = A XOR B, C = A AND B.
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Full Adder
A combinational circuit that adds three binary digits (A, B, and a Carry-in, Cin) and produces two outputs: Sum (S) and Carry-out (Cout). It can be built from two half adders and an OR gate.
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SR Flip-Flop
A basic sequential circuit with two inputs, Set (S) and Reset (R). S=1 sets the output Q to 1, R=1 resets Q to 0. S=1 and R=1 simultaneously is an invalid state.
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D-type Flip-Flop
A clocked sequential circuit that transfers the value of its data input (D) to its output (Q) on the triggering edge of a clock signal. It's used to store one bit of data and prevents the invalid state of an SR flip-flop.