However, it is still a little more complex than before. First of all, it takes longer. There is also the problem with the size of numbers (even more so than addition and subtraction!) 99 times 99 is 9801. A byte times a byte can result in a word! Multiplying two n-digit numbers will probably result in a 2n-digit number. Division goes the other direction, but is even more difficult because we have to keep track of the remainder. Then comes the wrinkle of signs!

So when you multiply two sixteen bit numbers, expect the answer to require more bits! The 80x86 CPU requires special registers for this:

Operand Size	Multi- plicand	Multiplier	Product
BYTE	AL	Reg or Memory	AX
WORD	AX	Reg or Memory Reg, immed Reg, Reg, immed	AX (low) and DX (high)
DWORD	EAX	Reg or memory Reg, immed Reg, Reg, immed	EAX (low) and EDX (high)

Where did this come from???? Well, it starts only with the 386 and works in the 16- or 32-bit mode on signed values only. It is a messy attempt to enhance things. Because of the nature of this mess, it is better not to use it (my opinion!)

Division is similar (except that it does not allow a constant!):

Operand Size	Dividend	Divisor	Quotient	Remainder
BYTE	AX	Reg or Memory	AL	AH
WORD	AX and DX	Reg or Memory	AX	DX

You can not use a constant operand with (sometimes )multiplication or (always) division. Use the mov instruction to put a constant into the appropriate register when needed.

Did I mention something about the sign? There are different instructions based on whether or not it is a signed or unsigned operation. That leads us to the following:

Yes, but....

• Since the multiplicand and dividend must be in the AX or AL or AX and DX, how do I keep them straight. Simply, let the computer do it! It is implied.
• When you need a word (or double word) and have a byte (or word), you must convert the value. There is a special set of instructions for that, because we need to make sure the number will continue to have the proper sign (without us having to write a lot of code.)
  

  cwd   ; convert the signed word in ax to a double word 
        ;   in ax and dx
  cbw   ; convert the signed byte in al to a word in ax
  cdq   ; convert the signed double word in eax to a quad word
        ;   (eight bytes) in edx, eax (higher order is in edx
        ;   ax is unchanged
  cwde  ; convert the signed word in ax to a double word
        ;   in eax
  

OK, lets put it together:

To do integer division with signed variables (word-sized)of miles driven, divided by number of gallons of gas used:

mov  ax, miles
cwd             ;ax is assumed
idiv gallons
mov  mpg, ax

To find out how many weeks and days are in a period of days, we could use unsigned bytes and do:

mov al, nrDays
sub ah, ah      ;don't sign extend because that 
                ;  would change the value
mov bl, 7
div bl          ;can't use a constant here!
mov weeks, al
mov days, ah    ;the remainder is the portion 
                ;  of a week

Very Important Reminders

• Multiplication and Division can only take place in the combination of registers in exactly the form described!
• You cannot multiply or divide directly by a constant. Move the constant to a register first.
• You must convert 8-bit dividends to 16-bit and 16-bit dividends to 32-bit.

UMBC | CSEE