Follow and write algorithms that use arithmetic operators (addition, subtraction, division, multiplication, modulus, integer division, exponentiation), relational operators (equal to, less than, greater than, not equal to, less than or equal to, greater than or equal to) and logical operators (AND, OR, NOT).

What this dot point is asking

Edexcel wants you to use the three families of operators in algorithms: arithmetic operators (including the two that GCSE students most often forget, modulus and integer division), relational operators that compare two values, and the logical operators AND, OR and NOT.

Arithmetic operators

The four basic operations are familiar, but Edexcel specifically lists integer division, modulus and exponentiation, and these are the ones questions probe.

• Integer division (DIV) returns only the whole-number quotient. $17 \text{ DIV } 5 = 3$, because 5 divides into 17 three whole times.
• Modulus (MOD) returns the remainder. $17 \text{ MOD } 5 = 2$, because $17 - (3 \times 5) = 2$.
• Exponentiation raises to a power: $3^2 = 9$ and $2^5 = 32$.

These two are extremely useful. MOD 2 tests whether a number is even (remainder 0) or odd (remainder 1). Together, DIV and MOD split a number into parts: to convert 197 seconds into minutes and seconds, $197 \text{ DIV } 60 = 3$ minutes and $197 \text{ MOD } 60 = 17$ seconds.

Relational operators

Relational operators are what conditions in selection and repetition are built from. if mark >= 40 then uses "greater than or equal to"; while guess != target uses "not equal to". A frequent mistake is to confuse assignment with the equality test: many languages use = (or <-) to assign a value and == to test equality, so read the context carefully. At GCSE the result of a relational operator is always a Boolean, which is then used by a selection or a loop.

Logical operators

Logical operators let a single condition test several things at once. if age >= 13 AND age <= 19 then is true only for teenagers, because both comparisons must hold. if day = "Saturday" OR day = "Sunday" then is true at the weekend, because only one needs to hold. if NOT logged_in then runs when the user is not logged in. Combining operators correctly, and getting AND versus OR right, is regularly tested and links directly to truth tables.

Operator precedence

When an expression mixes operators, they are applied in a set order, just as in maths. Exponentiation is done first, then multiplication, division, integer division and modulus, then addition and subtraction, and finally the relational and logical operators. Brackets override this order, so $2 + 3 \times 4 = 14$ but $(2 + 3) \times 4 = 20$. When in doubt in an algorithm, add brackets to make the intended order explicit; this also makes the code easier to read.

Try this

Q1. State the result of $23 \text{ MOD } 4$. [1 mark]

• Cue. 3, because $23 - (5 \times 4) = 3$.

Q2. Write a condition that is true only when a number n is greater than 0 and even. [2 marks]

• Cue. n > 0 AND n MOD 2 = 0.