# MOD

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

## Syntax

*remainder*=*numerator*MOD*divisor*

## Parameters

- Returns the integer division remainder as a whole INTEGER, LONG or _INTEGER64 value.
*numerator*is the INTEGER value to divide.*divisor*is the INTEGER value to divide by.

## 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.
. This will create a "Division by zero" error due to CINT rounding the value to 0.*divisor*(second value) must not be between 0 and .5- 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).

## See also

- / (normal division operator)
- \ (integer division operator)
- INT, CINT, FIX, _ROUND, _CEIL
- Mathematical Operations

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