# Boolean

**Boolean** statements are numerical evaluations that return True (-1 or NOT 0) or False (0) values that can be used in other calculations.

*Basic Returns:*

- True evaluations return -1. NOT 0 = -1 in Basic. Can be used to increment a value.
- For positive True results, subtract it, multiply it by a negative value or use ABS.
- False evaluations return 0. Watch out for "Division by 0" errors!

**Relational Operators:**

Symbol | Condition | Example Usage |
---|---|---|

< | Less than | IF a < b THEN |

> | Greater than | IF a > b THEN |

= | Equal | IF a = b THEN |

<= | Less than or equal | IF a <= b THEN |

>= | Greater than or equal | IF a >= b THEN |

<> | NOT equal | IF a <> b THEN |

- When evaluating a True value, an IF value < 0 statement is NOT necessary for return values not 0.

**Truth table of the BASIC Logical Operators:**

*A*and

*B*are operands, and

*T*and

*F*indicate that a bit is set or not set:

Operands Operations A B `NOT B``A AND B``A OR B``A XOR B``A EQV B``A IMP B`T T F T T F T T T F T F T T F F F T F F T T F T F F T F F F T T

**Relational Operations return negative one (-1, all bits set) and zero (0, no bits set) for**

*true*and*false*, respectively.

**Boolean Conditional Operators:**

- AND can be used to add extra conditions to a boolean statement evaluation. Both must be True.
- OR can be used to add alternate conditions to a boolean statement evaluation. One must be True.
- Parenthesis are allowed inside of boolean statements to clarify an evaluation.
**Note that Basic returns -1 for True and 0 for False.**

*Example 1:* Using 2 different boolean evaluations to determine a leap year.

* *
INPUT "Enter a year greater than 1583: ", annum$
Y = VAL(annum$)
leap1 = (Y MOD 4 = 0 AND Y MOD 100 <> 0) OR (Y MOD 400 = 0)
leap2 = (Y MOD 4 = 0) - (Y MOD 100 = 0) + (Y MOD 400 = 0)
PRINT "Year = "; annum$, "Leap1 = "; leap1, "Leap2 = "; leap2 * *

*Explanation:*Both boolean evaluations will return -1 if the year is a leap year. It is not simply every four years as many people think. That is checked by the first evaluation (Y MOD 4 = 0) of each. In new century years like 1900 (which was not a leapyear) there is only one leap year every 400 years. 100 is used with MOD to see if there is a remainder. When that is true, the boolean return of that part of the first evaluation will be 0. The second returns -1 (which is actually added). In both evaluations the result of (Y MOD 400 = 0) indicates a century leap year.

- Entry year = 2000:

- leap1 = (-1 AND 0) OR -1 = -1 ' the AND evaluation returns False(0) so the OR value is used.
- leap2 = (-1) - (-1) + (-1) = -1 + 1 + -1 = -1

- Entry year = 1900:

- leap1 = (-1 AND 0) OR 0 = 0 OR 0 = 0
- leap2 = (-1) - (-1) + (0) = -1 + 1 + 0 = 0

*Example 2:* Moving an ASCII character using the arrow keys and boolean statements to determine the new coordinate.

* *
SCREEN 12
COLOR 7
LOCATE 11, 20: PRINT "Using Screen 12 here to be in 80 X 30 coordinates mode"
LOCATE 13, 6: PRINT "Simple Example of Alternative programming without IF-THEN-ELSE Statements"
LOCATE 15, 1: PRINT "Use the four Cursor keys to move the yellow cursor, text will not be disturbed"
LOCATE 17, 12: PRINT "When you END the program with the ESC key, cursor will disappear"
cordx% = 40
cordy% = 15
DO
oldcordx% = cordx%
oldcordy% = cordy%
p% = SCREEN(cordy%, cordx%) 'get ASCII character code at present position
COLOR 14: LOCATE cordy%, cordx%: PRINT CHR$(178); 'print cursor character to position
WHILE cordx% = oldcordx% AND cordy% = oldcordy% AND k$ <> CHR$(27)
k$ = INKEY$
cordx% = cordx% + (k$ = (CHR$(0) + "K") AND cordx% > 1) + ABS(k$ = (CHR$(0) + "M") AND cordx% < 80)
cordy% = cordy% + (k$ = (CHR$(0) + "H") AND cordy% > 1) + ABS(k$ = (CHR$(0) + "P") AND cordy% < 30)
WEND
COLOR 7: LOCATE oldcordy%, oldcordx%: PRINT CHR$(p%); 'replace overwritten screen characters
LOOP UNTIL k$ = CHR$(27) * *

*See also:*

*Navigation:*