Sums

Introduction

A computer is, underneath, a machine for sums, and BBC BASIC will do yours at the > or in a program. Most of it is what you would expect. A little of it is not, and those are the parts worth knowing before a program depends on them.

The Six Operators

Sign	Does	`7` and `2` give
`+`	adds	`9`
`-`	subtracts	`5`
`*`	multiplies	`14`
`/`	divides	`3.5`
`DIV`	divides, keeping only the whole number	`3`
`MOD`	the remainder after that	`1`
`^`	raises to a power: `2^10` is 2 times itself ten times	`1024`

Multiply is *, not x. DIV and MOD are words, with a space either side: 7 DIV 2.

DIV and MOD belong together. Share 100 sweets among 7 people and 100 DIV 7 is how many each person gets, 100 MOD 7 how many are left over.

Which Comes First

2+3*4 is 14, not 20. Multiplying and dividing - *, /, DIV, MOD - are done before adding and subtracting, and brackets come before either: (2+3)*4 is 20. When in doubt, bracket it: brackets never hurt.

Things of the same rank are done from left to right, so 10-4-3 is 3.

Two cases catch people out, so try them once:

2^3^2 is 64. The powers are done left to right too: 2 cubed is 8, and 8 squared is 64.
-2^2 is 4, not -4. The minus sign belongs to the 2 before the power is worked out. If you mean "minus two squared", write -(2^2).

How Answers Are Printed

A number printed on its own is lined up on the right of a ten-column space, which is why PRINT 7+3 puts 10 well over from the left. When you print a column of answers, the units line up under each other - that is the point of it.

Fractions get nine significant figures: 1/3 prints as 0.333333333.

Very big and very small numbers are printed in E notation. 1.23456789E9 means 1.23456789 times ten to the power 9 - move the point nine places right to get 1234567890. Whole numbers switch to this at ten digits, and small ones sooner: 0.001 prints as 1E-3.

The Code

10 PRINT 7+3
20 PRINT 7-3
30 PRINT 7*3
40 PRINT 7/2
50 PRINT 7 DIV 2
60 PRINT 7 MOD 2
70 PRINT 2^10
80 PRINT 2+3*4
90 PRINT (2+3)*4

Starting from

A fresh boot, or NEW.

What you should see

The sums, right-aligned

Change One Thing

Change line 40 to PRINT 1/3. How many 3s do you get?
Change line 70 to PRINT 2^40. What does the answer mean?
At the >, try PRINT 2^3^2 and then PRINT -2^2. Are they what you expected? Why not?

Exercises

7.1 How many seconds are there in a day? Make BBC BASIC work it out.

7.2 100 sweets are shared among 7 children. Print how many each gets and how many are left over, on one line.

7.3 Print the average of 4, 8 and 9.

Worked solutions are in Appendix II.

When It Goes Wrong

Symptom	Cause
`Division by zero`	Something was divided by 0.
A minus sum prints only the first number, then `No such variable`	The key marked `-` types `_`. Minus is SHIFT and `=`.
`-2^2` prints `4`	The minus belongs to the 2. Write `-(2^2)`.
A big number prints as something like `1.23456789E9`	That is E notation - move the point 9 places right.
`7 DIV 2*2` is 6, not 1	`DIV` ranks with ``, so it is done first, left to right. Bracket what you mean: `7 DIV (22)`.

Summary

+ - * / as usual; DIV and MOD for whole-number division and remainders; ^ for powers. Multiplying and dividing come before adding and subtracting, brackets first, and otherwise left to right. Numbers print right-aligned in ten columns, to nine figures, in E notation when they are very big or small.

S8, Names For Numbers - keeping an answer under a name, so a program can use it again.

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