# MOD

The MOD operator gives the remainder after division of one number by another (sometimes called modulus).

## Syntax

remainder = numerator MOD divisor

## Description

• Floating decimal point numerator and divisor values are CINT rounded (e.g. 19 MOD 6.7 returns 5 just like 19 MOD 7 would).
• MOD returns 0 if a number is evenly divisible by integer division ( \ ) or the number divided is 0.
• divisor (second value) must not be between 0 and .5. This will create a "Division by zero" error due to CINT rounding the value to 0.
• The result has the same sign as the numerator (e.g. -1 MOD 7 returns -1, not 6).
• Division and multiplication operations are performed before addition and subtraction in QBasic's order of operations.

## Examples

Example 1:

I% = 100 \ 9 R% = 100 MOD 9 PRINT "Integer division ="; I%, "Remainder ="; R%

Integer division = 11 Remainder = 1

Explanation: Integer division 100 \ 9 returns 11. 11 * 9 = 99. So the remainder must be 1 as 100 - 99 = 1. Normal decimal point division would return 11.11111.

Example 2: Comparing normal, integer and remainder division.

tmp1\$ = " Normal: ####.# / #### = ##.### " tmp2\$ = " Integer: ####.# \ #### = ### " tmp3\$ = " Remainder: ####.# MOD #### = #### " FOR i = 1 TO 6 SELECT CASE i CASE 1: numerator = 1: divisor = 5 CASE 2: numerator = 13: divisor = 10 CASE 3: numerator = 990: divisor = 100 CASE 4: numerator = 1100: divisor = 100 CASE 5: numerator = 4501: divisor = 1000 CASE 6: numerator = 50.6: divisor = 10 END SELECT LOCATE 5, 20: PRINT USING tmp1\$; numerator; divisor; numerator / divisor LOCATE 7, 20: PRINT USING tmp2\$; numerator; divisor; numerator \ divisor LOCATE 9, 20: PRINT USING tmp3\$; numerator; divisor; numerator MOD divisor DO: SLEEP: LOOP UNTIL INKEY\$ <> "" NEXT

Example 3: Integer division and MOD can be used to convert values to different base numbering systems from base 2 to 36 as strings:

CLS DO INPUT "Enter a base number system 2 to 36: ", b% IF b% < 2 OR b% > 36 THEN EXIT DO PRINT "Enter a positive value to convert: "; num\$ = "" DO: K\$ = INKEY\$ num\$ = num\$ + K\$ LOCATE CSRLIN, POS(0): PRINT K\$; LOOP UNTIL K\$ = CHR\$(13) n& = VAL(num\$) IF n& = 0 THEN EXIT DO Bnum\$ = BASEN\$(n&, b%) PRINT Bnum\$ ', VAL("&H" + Bnum\$) 'tests hexadecimal base 16 only LOOP END FUNCTION BASEN\$ (number&, basenum%) IF basenum% < 2 OR basenum% > 36 OR number& = 0 THEN EXIT FUNCTION num& = number& 'protect value of number! DO remain% = ABS(num&) MOD basenum% ' remainder is used to create actual digit 0 to Z num& = num& \ basenum% ' move up one exponent of base% with integer division IF remain% > 9 THEN b\$ = CHR\$(65 + (remain% - 10)) 'limited to base 36 ELSE: b\$ = LTRIM\$(STR\$(remain%)) ' make remainder a string number END IF BN\$ = b\$ + BN\$ ' add remainder character to base number string LOOP UNTIL num& = 0 BASEN\$ = BN\$ END FUNCTION

Note: Base numbering systems over base 10(0 - 9) use alphabetical letters to represent digits greater than 9 like Hexadecimal(0 - F).