IB Computer Science - 2.1.11-13 Boolean Operators, Truth Tables, Logic Diagram

2.1.11-13 Boolean Operators,

2.1.11 Define the Boolean operators: AND, OR, NOT, NAND, NOR and XOR.

2.1.12 Construct truth tables using the above operators.

2.1.13Construct a logic diagram using AND, OR, NOT, NAND, NOR and XOR gates.

A device that performs a basic operation on electrical signals

Gates combined to perform more complicated tasks

Uses Boolean algebra, a mathematical notation for expressing two-valued logic

A graphical representation of a circuit

Each gate has its own symbol

A table showing all possible input values and the associated output values

A NOT gate accepts one input signal (0 or 1) and returns the complementary (opposite) signal as output

An AND gate accepts two input signals

If both are 1, the output is 1; otherwise,

the output is 0

An OR gate accepts two input signals

If both are 0, the output is 0; otherwise,

the output is 1

An XOR gate accepts two input signals

If both are the same, the output is 0; otherwise, the output is 1

The NAND (“NOT of AND”) gate accepts two input signals

If both are 1, the output is 0; otherwise,

the output is 1

The NOR (“NOT of OR”) gate accepts two inputs

If both are 0, the output is 1; otherwise,

the output is 0

Some gates can be generalized to accept three or more input values

A three-input AND gate, for example, produces an output of 1 only if all input values are 1

1. (A * B)’ * (B + C) * C’

2. (A + B) + (B’ ⊕ C )

3. A’ ⊕ (B * C)’

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