F1 · Boolean Logic and F2 · Flow Charts

Spec reference: Sections F1 and F2 - Logic and Data Flow Key idea: Use Boolean logic and flow charts to represent and solve data flow problems in computer systems.

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Boolean logic

Boolean logic uses two values: TRUE (1) and FALSE (0). All decisions in a computer system are made using combinations of these values.

Logic gates

Gate	Symbol description	Operation	Truth table
AND	Both inputs must be 1	A AND B	Output is 1 only if A=1 AND B=1
OR	At least one input is 1	A OR B	Output is 1 if A=1 OR B=1 (or both)
NOT	Inverts the input	NOT A	Output is 1 if A=0; output is 0 if A=1
NAND	AND followed by NOT	NOT(A AND B)	Output is 0 only if both A=1 AND B=1
NOR	OR followed by NOT	NOT(A OR B)	Output is 1 only if both A=0 AND B=0
XOR	Exclusive OR	A XOR B	Output is 1 if inputs are different

Truth tables

AND gate:

A	B	A AND B
0	0	0
0	1	0
1	0	0
1	1	1

OR gate:

A	B	A OR B
0	0	0
0	1	1
1	0	1
1	1	1

NOT gate:

A	NOT A
0	1
1	0

XOR gate:

A	B	A XOR B
0	0	0
0	1	1
1	0	1
1	1	0

Boolean expressions

Logic can be written as expressions:

Expression	Meaning
$A\cdot B$ or $A\text{ AND }B$	AND
$A+B$ or $A\text{ OR }B$	OR
$\bar{A}$ or $\text{NOT }A$	NOT

Example: A security door opens if the user has a valid card AND the PIN is correct AND it is not outside working hours.

$$\text{Open}=\text{ValidCard}\cdot \text{CorrectPIN}\cdot \overline{\text{OutsideHours}}$$

Boolean laws

Law	Expression
Identity	$A+0=A$, $A\cdot 1=A$
Null	$A+1=1$, $A\cdot 0=0$
Idempotent	$A+A=A$, $A\cdot A=A$
Complement	$A+\bar{A}=1$, $A\cdot \bar{A}=0$
De Morgan's	$\overline{A\cdot B}=\bar{A}+\bar{B}$, $\overline{A+B}=\bar{A}\cdot \bar{B}$

De Morgan's theorem

De Morgan's is commonly tested. It says: the NOT of an AND is the same as the OR of the NOTs. And vice versa.

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Flow charts and system diagrams

Flow charts represent the step-by-step logic of a process or system visually.

Flow chart symbols

Symbol	Shape	Used for
Terminator	Rounded rectangle	START and END
Process	Rectangle	An operation or calculation
Decision	Diamond	A yes/no question branching the flow
Input/Output	Parallelogram	Reading input or displaying output
Flow arrow	Arrow	Shows the direction of flow

Flow chart rules

• Every flow chart must have exactly one START and at least one END.
• Decision diamonds must have exactly two labelled exits: Yes and No (or True and False).
• Compass arcs must remain visible in exam constructions.
• Flow charts should be unambiguous: every path must eventually lead to an END.

Example: Login system

START
  |
  v
Input username and password
  |
  v
<Valid credentials?> --No--> Display error message --> END
  | Yes
  v
Grant access
  |
  v
END

System diagrams

System diagrams show how data flows between different components of a system. They are used to represent:

• Input sources and output destinations.
• Processes that transform data.
• Storage components.
• Communication links between systems.

Data flow diagram (DFD) notation:

• Rectangle: External entity (person, system).
• Rounded rectangle / oval: Process.
• Open rectangle (two parallel lines): Data store.
• Arrow: Data flow, labelled with the data being transferred.

Exam approach

When asked to draw or complete a flow chart, check that every decision has two clearly labelled exits and that every path leads to a terminator. Missing labels or dangling arrows lose marks.

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Summary

Term	Meaning
AND gate	Output is 1 only when all inputs are 1
OR gate	Output is 1 when at least one input is 1
NOT gate	Inverts the input
XOR gate	Output is 1 when inputs are different
De Morgan's theorem	NOT(A AND B) = (NOT A) OR (NOT B)
Decision diamond	Flow chart symbol for a yes/no branch
DFD	Diagram showing how data flows through a system

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