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

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Title: Basic Pascal Tutorial/Chapter 3/Boolean Expressions

New		Line
1	+	3B - Boolean Expressions (author: Tao Yue, state: unchanged)
2	+
3	+	[[Boolean]] expressions are used to compare two values and get a `true-or-false` answer:
4	+
5	+	`value1 ``relational_operator`` value2`
6	+
7	+	The following relational operators are used:
8	+
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`
15	+
16	+	You can assign Boolean expressions to Boolean variables. Here we assign a `true` expression to some_bool:
17	+
18	+	``` pascal
19	+	some_bool := 3 < 5;
20	+	```
21	+
22	+	Complex Boolean expressions are formed by using the Boolean operators:
23	+
24	+	`not negation (~)`\
25	+	`and conjunction (^)`\
26	+	`or disjunction (v)`\
27	+	`xor exclusive-or`
28	+
29	+	`NOT` is a unary operator — it is applied to only one value and inverts it:
30	+
31	+	- <tt>not true = false
32	+	- not false = true</tt>
33	+
34	+	`AND` yields `TRUE` only if both values are `TRUE`:
35	+
36	+	- <tt>TRUE and FALSE = FALSE
37	+	- TRUE and TRUE = TRUE</tt>
38	+
39	+	`OR` yields `TRUE` if at least one value is `TRUE`:
40	+
41	+	- <tt>TRUE or TRUE = TRUE
42	+	- TRUE or FALSE = TRUE
43	+	- FALSE or TRUE = TRUE
44	+	- FALSE or FALSE = FALSE</tt>
45	+
46	+	`XOR` yields `TRUE` if one expression is `TRUE` and the other is `FALSE`. Thus:
47	+
48	+	- <tt>TRUE xor TRUE = FALSE
49	+	- TRUE xor FALSE = TRUE
50	+	- FALSE xor TRUE = TRUE
51	+	- FALSE xor FALSE = FALSE</tt>
52	+
53	+	When combining two Boolean expressions using relational and Boolean operators, be careful to use parentheses.
54	+
55	+	``` pascal
56	+	(3>5) or (650<1)
57	+	```
58	+
59	+	This is because the Boolean operators are higher on the order of operations than the relational operators:
60	+
61	+	1. <tt>not
62	+	2. * / div mod and
63	+	3. \+ - or
64	+	4. \< \> \<= \>= = \<\></tt>
65	+
66	+	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	+
68	+	The Boolean operators (`AND, OR, NOT, XOR`) can be used on Boolean variables just as easily as they are used on Boolean expressions.
69	+
70	+	Whenever possible, don't compare two real values with the equals sign. Small round-off errors may cause two equivalent expressions to differ.
71	+
72	+	---
73	+	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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