Relational Operators

Comparisons produce True or False

A program often needs to decide whether something is the case: has a player reached a target score, are two answers the same, or is one value larger than another?

A relational operator compares two values. The result is a Boolean value: either True or False. For example, 4 < 6 evaluates to True, while 6 < 4 evaluates to False. The result is not a number showing the difference between the values; it tells us whether the comparison is true.

A comparison can use literal values, variables or expressions. If score currently holds 12, then score > 10 evaluates to True. If the value of score changes, the result of that comparison may change too.

The six relational operators

AQA pseudo-code uses these symbols:

Read each comparison from left to right. score ≥ target means that the score is greater than or equal to the target.

The equality part matters at a boundary. Suppose a player qualifies with a score of at least 10. The condition is score ≥ 10: a score of exactly 10 qualifies. Using score > 10 would exclude that score. Similarly, “fewer than 10” means < 10, whereas “no more than 10” means ≤ 10.

Comparing values is different from assigning them

A variable is a named storage location whose value can change. Assignment puts a value into that variable; comparison tests a relationship between values.

score ← 10
score = 10

The first line stores 10 in score. The second expression tests whether score equals 10 and evaluates to True. It does not change the value of score.

Different programming languages use different symbols for the same comparisons. For example:

Thus, AQA’s score ≥ 10 and Python’s score >= 10 test the same relationship. To interpret an algorithm, recognise the operation’s meaning rather than relying only on how its symbol looks.

Evaluating expressions and ordering other data

When a comparison contains arithmetic, calculate the arithmetic values first, then compare them. For example:

• (3 * 4) ≤ 15 becomes 12 ≤ 15, so the result is True.
• (15 MOD 2) = 0 becomes 1 = 0, so the result is False.
• (50 - 40) > (3 * (2 + 5)) becomes 10 > 21, so the result is False.

Brackets make the intended calculations easier to read.

Comparisons are not restricted to integers. Real numbers can be compared too: 4.1 > 4.0 is True, and 4.5 ≥ 4.5 is also True.

Characters and strings can have an order. For example, 'A' < 'B' is True. Strings can be compared in lexicographic order, like dictionary order. Compare their characters from left to right until a difference determines which comes first: 'adam' < 'adele' is True because their first two letters match, then a comes before e. Use values of appropriate, compatible data types rather than assuming that any two kinds of data can be meaningfully ordered.

Using a comparison to make a decision

A condition is an expression that evaluates to True or False. In selection, it determines whether a block of instructions runs.

Suppose a game awards a qualification message for reaching a target score:

score ← 10
targetScore ← 10
IF score ≥ targetScore THEN
    OUTPUT 'Qualified'
ENDIF

Substituting the current values gives 10 ≥ 10, which is True, so the message is output. With a score of 9, the condition would be False and the output instruction would be skipped.

To construct a condition, identify the two values being compared, decide which relationship expresses the rule, and check what should happen when the values are equal.

Following comparisons as an algorithm runs

In condition-controlled iteration, a comparison can determine whether instructions repeat. Its result must be checked using the latest variable values.

number ← 1
WHILE number < 4
    OUTPUT number
    number ← number + 1
ENDWHILE

The condition is initially 1 < 4, so the program outputs 1 and changes number to 2. It then checks the condition again.

The output is therefore 1, 2, 3. The final value of number is 4, but 4 is not output because the comparison becomes False before the output instruction runs again.

A REPEAT–UNTIL loop uses a stopping condition instead:

number ← 1
REPEAT
    OUTPUT number
    number ← number + 1
UNTIL number = 4

Here, the equality comparison is checked after the instructions. Once number becomes 4, number = 4 is True and repetition stops. This also outputs 1, 2, 3. The key distinction is that WHILE repeats while its condition is true, whereas UNTIL ends repetition when its condition is true.