GCSE OCR Computer Science: Logic Diagrams and Truth Tables

Logic Diagrams and Truth Tables

Binary situations in daily life and computing represent states that can only be in one of two conditions (e.g., Stop/Go, On/Off).
In computing terms:
- A binary $1$ represents True.
- A binary $0$ represents False.
Boolean operators ( $AND$ , $OR$ , $NOT$ ) are used in programming constructs such as $IF$ statements and $while$ loops.

The Three Fundamental Logic Gates

AND Gate:
- Logic statement: $P = A \text{ AND } B$
- Output is $1$ (True) only if both inputs are $1$ .
OR Gate:
- Logic statement: $P = A \text{ OR } B$
- Output is $1$ (True) if either input is $1$ .
NOT Gate:
- Logic statement: $P = \text{NOT } A$
- Output is the opposite of the input (inversion).

Truth Tables

A truth table displays the output for all possible combinations of inputs from a Boolean expression.
For two inputs ( $A$ and $B$ ), there are four possible combinations:

AND Truth Table

Input $A$	Input $B$	Output $P$
$0$	$0$	$0$
$0$	$1$	$0$
$1$	$0$	$0$
$1$	$1$	$1$

OR Truth Table

Input $A$	Input $B$	Output $P$
$0$	$0$	$0$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$1$

NOT Truth Table

Input $A$	Output $P$
$0$	$1$
$1$	$0$

Logic Statement Evaluations

(4 > 3) \text{ AND } (5 > 7): False
(2 < 8) \text{ OR } (8 > 10): True
\text{NOT } (5 \times 7 > 30): False
$(((7 \text{ DIV } 3) \geq 2) \text{ OR } ((7 \text{ DIV } 3) < 2)): True\n- $(((12 \text{ MOD } 5) < 2) \text{ AND } ((12 \text{ MOD } 5) == 2)): False
Note: $\text{DIV}$ gives integer division; $\text{MOD}$ gives the remainder.

Combining Logic Gates

Complex circuits can be built by combining fundamental gates.
Example: Security Lighting
- Logic requirement: The light ( $P$ ) must come on if it senses movement ( $S$ ) AND it is night time ( $N$ ), OR if a manual override button ( $B$ ) is pressed.
- Logic Statement: $P = (S \text{ AND } N) \text{ OR } B$
- Intermediate result ( $R$ ) represents $S \text{ AND } N$ .

Questions & Discussion

Starter Activity: The Safe Problem

Prompt: Consider a safe with two keys. If both keys are used, the safe will open ( $if \text{ key1 AND key2 then safeOpen = True else safeOpen = False}$ ). What are the only possible values that key1 and key2 can be?
Response: They can only be True or False (lock or unlock).
Prompt: What values must they be to open the safe?
Response: They must both be True.

Plenary Review

Question: What are the three basic logic gates?
Answer: $AND$ , $OR$ , and $NOT$ .
Question: Explain what each logic gate does.
Answer: $AND$ requires both inputs to be True for a True output; $OR$ requires at least one input to be True; $NOT$ outputs the opposite of the input.
Question: What is a truth table?
Answer: It shows all possible combinations of inputs and the outputs they create.