Thinking Logically

Thinking logically means identifying decision points in a problem, determining the conditions that govern each decision, using logical reasoning to predict outcomes, and applying logic to debug programs. This is a core part of OCR H446 section 2.1.

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What Is Logical Thinking?

Logical thinking in Computer Science is about making decisions based on conditions. Every program contains decision points where the flow of execution depends on whether a condition is true or false.

Concept	Definition
Decision point	A place in an algorithm where the next step depends on a condition
Condition	A Boolean expression that evaluates to TRUE or FALSE
Logical reasoning	Using conditions and rules to determine what will happen

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Identifying Decision Points

Decision points appear whenever there is a choice or branch in an algorithm:

Structure	Decision	Example
IF-THEN-ELSE	Choose between two paths	IF age >= 18 THEN grant access ELSE deny access
WHILE loop	Continue or stop	WHILE password incorrect DO ask again
FOR loop	Implicit decision at each iteration	FOR i = 0 TO n-1 (implicitly checks i < n)
CASE/SWITCH	Choose among multiple paths	CASE grade OF "A": distinction, "B": merit, etc.
Exception handling	Handle error or continue normally	TRY ... CATCH if file not found

Worked Example — ATM Withdrawal:

1. User inserts card
2. DECISION: Is the card valid? (Yes/No)
3. User enters PIN
4. DECISION: Is the PIN correct? (Yes/No)
5. DECISION: Has the user exceeded maximum attempts? (Yes/No)
6. User selects amount
7. DECISION: Is the amount <= account balance? (Yes/No)
8. DECISION: Does the machine have enough cash? (Yes/No)
9. Dispense cash
10. Update balance

Each DECISION is a decision point with a condition that must be evaluated.

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Determining Conditions

For each decision point, you must specify the exact condition being tested:

Decision point	Condition	Data type
User is an adult	age >= 18	Integer comparison
Password is correct	enteredPassword = storedHash	String comparison
List is empty	length(list) = 0	Integer comparison
Item exists in database	searchResult != NULL	Null check
Temperature is dangerous	temp > 100 OR temp < -20	Compound Boolean

Compound conditions use AND, OR, and NOT to combine simple conditions:

Compound condition	Meaning
age >= 18 AND hasID = TRUE	Both must be true
isStudent = TRUE OR isStaff = TRUE	At least one must be true
NOT(fileExists)	The file must not exist
(score >= 40) AND (coursework >= 30) AND (attendance >= 80)	All three must be true to pass

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Logical Reasoning and Predicting Outcomes

Logical reasoning allows you to trace through an algorithm and predict the output without running it.

Trace table example:

Given:

x = 5
y = 3
WHILE x > 0
    IF x MOD 2 = 1 THEN
        y = y + x
    ELSE
        y = y - 1
    END IF
    x = x - 1
END WHILE
OUTPUT y

Trace:

Iteration	x (start)	x MOD 2 = 1?	y (after)	x (after)
1	5	Yes (5 is odd)	3 + 5 = 8	4
2	4	No (4 is even)	8 - 1 = 7	3
3	3	Yes (3 is odd)	7 + 3 = 10	2
4	2	No (2 is even)	10 - 1 = 9	1
5	1	Yes (1 is odd)	9 + 1 = 10	0

x is now 0, so the loop ends. Output: 10.