Basic Pascal Tutorial/Chapter 3/Boolean Expressions: what changed

Revision 2 to 3. Removed lines have a minus sign; added lines have a plus sign.

Old	New		Line
1	1		3B - Boolean Expressions (author: Tao Yue, state: unchanged)
2	2
3	3		[[Boolean]] expressions are used to compare two values and get a `true-or-false` answer:
4	4
5		-	~~`value1 ``relational_operator`` value2`~~
	5	+	```
	6	+	value1 relational_operator value2
	7	+	```
6	8
7	9		The following relational operators are used:
8	10
9		-	~~`< less than`\~~
10		-	~~`> greater than`\~~
11		-	~~`= equal to`\~~
12		-	~~`<= less than or equal to`\~~
13		-	~~`>= greater than or equal to`\~~
14		-	~~`<> not equal to`~~
	11	+	```
	12	+	< less than
	13	+	> greater than
	14	+	= equal to
	15	+	<= less than or equal to
	16	+	>= greater than or equal to
	17	+	<> not equal to
	18	+	```
15	19
16	20		You can assign Boolean expressions to Boolean variables. Here we assign a `true` expression to some_bool:
17	21
18	22		``` pascal
19	23		some_bool := 3 < 5;
20	24		```
21	25
22	26		Complex Boolean expressions are formed by using the Boolean operators:
23	27
24		-	~~`not negation (~)`\~~
25		-	~~`and conjunction (^)`\~~
26		-	~~`or disjunction (v)`\~~
27		-	~~`xor exclusive-or`~~
	28	+	```
	29	+	not negation (~)
	30	+	and conjunction (^)
	31	+	or disjunction (v)
	32	+	xor exclusive-or
	33	+	```
28	34
29	35		`NOT` is a unary operator — it is applied to only one value and inverts it:
30	36
31	37		- not true = false
32	38		- not false = true
33	39
34	40		`AND` yields `TRUE` only if both values are `TRUE`:
35	41
36	42		- TRUE and FALSE = FALSE
37	43		- TRUE and TRUE = TRUE
38	44
39	45		`OR` yields `TRUE` if at least one value is `TRUE`:
40	46
41	47		- TRUE or TRUE = TRUE
42	48		- TRUE or FALSE = TRUE
43	49		- FALSE or TRUE = TRUE
44	50		- FALSE or FALSE = FALSE
45	51
46	52		`XOR` yields `TRUE` if one expression is `TRUE` and the other is `FALSE`. Thus:
47	53
48	54		- TRUE xor TRUE = FALSE
49	55		- TRUE xor FALSE = TRUE
50	56		- FALSE xor TRUE = TRUE
51	57		- FALSE xor FALSE = FALSE
52	58
53	59		When combining two Boolean expressions using relational and Boolean operators, be careful to use parentheses.
54	60
55	61		``` pascal
56	62		(3>5) or (650<1)
57	63		```
58	64
59	65		This is because the Boolean operators are higher on the order of operations than the relational operators:
60	66
61	67		1. not
62	68		2. * / div mod and
63	69		3. \+ - or
64	70		4. \< \> \<= \>= = \<\>
65	71
66	72		So `3 > 5 or 650 < 1` becomes evaluated as `3 > (5 or 650) < 1`, which makes no sense, because the Boolean operator or only works on Boolean values, not on integers.
67	73
68	74		The Boolean operators (`AND, OR, NOT, XOR`) can be used on Boolean variables just as easily as they are used on Boolean expressions.
69	75
70	76		Whenever possible, don't compare two real values with the equals sign. Small round-off errors may cause two equivalent expressions to differ.
71	77
72	78		---
73	79		From the Free Pascal wiki, page "Basic Pascal Tutorial/Chapter 3/Boolean Expressions", as it stood on 2022-08-20 after a change by Kai Burghardt, out of the wiki's dump of 2024-05-26. Copyright stays with the author who wrote it, according to the old wiki's [[Licensing]] page. If you have concerns about this material, [message the admin](/wiki-contact).

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