Curriculum Portal

neurologyYou need to know

• Boolean logic represents two possible states: `1` means true and `0` means false.
• An AND gate, also called conjunction, outputs `1` only when all of its inputs are `1`.
• For an AND gate, the outputs for input pairs `00`, `01`, `10` and `11` are respectively `0`, `0`, `0` and `1`.
• An OR gate, also called disjunction, outputs `1` when at least one of its inputs is `1`.
• For an OR gate, the outputs for input pairs `00`, `01`, `10` and `11` are respectively `0`, `1`, `1` and `1`.
• A NOT gate, also called negation or an inverter, has one input and outputs the opposite Boolean value.
• For a NOT gate, an input of `0` produces `1`, while an input of `1` produces `0`.
• The standard AND gate symbol has a flat input side and a curved output side, while the standard OR gate symbol has a curved input side and a pointed output side.
• The standard NOT gate symbol is a triangle with a small inversion circle at its output.
• A truth table lists every possible combination of input values and the corresponding output value or values.
• A logic circuit with `n` independent Boolean inputs has `2^n` possible input combinations, so its truth table requires `2^n` rows.
• Boolean operators can be combined so that the output from one gate becomes the input to another gate.
• An inversion circle on a gate or connection indicates that the associated Boolean value is negated.
• In the expression `(A \mathbin{\mathrm{AND}} B) \mathbin{\mathrm{OR}} (\mathbin{\mathrm{NOT}} C)`, the intermediate results of `A \mathbin{\mathrm{AND}} B` and `\mathbin{\mathrm{NOT}} C` are inputs to the final OR operation.
• Alternative Boolean notation may use `T` and `F` instead of `1` and `0`, and symbols such as `\land`, `\lor` and `\lnot` for AND, OR and NOT respectively.

• Recognise AND, OR and NOT gates from their standard logic-gate symbols.
• Complete the truth table for an AND, OR or NOT gate by applying the correct rule to every input combination.
• Construct a truth table containing all `2^n` input combinations for a circuit with `n` independent inputs.
• Trace a multi-gate logic diagram in sequence, recording each intermediate gate output before calculating the final output.
• Create a logic diagram from a Boolean expression or written scenario, connecting gates in the correct order.
• Derive a Boolean expression from a given logic diagram, using brackets to show how operators are combined.
• Edit a logic diagram or truth table so that it produces the outputs required by a stated scenario.
• Apply AND, OR and NOT operators to solve Boolean problems and justify each final output using intermediate values or a completed truth table.