Multiplication and Division Instructions Multiplication and Division Instructions
• MUL Instruction
• IMUL Instruction
• DIV Instruction
• Signed Integer Division
• Implementing Arithmetic Expressions
MUL Instruction MUL Instruction
• The MUL (unsigned multiply) instruction multiplies an 8-, 16-, or 32-bit operand by either AL, AX, or EAX.
• The instruction formats are:
MUL r/m8 MUL r/m16 MUL r/m32
Implied operands:
MUL Examples MUL Examples
100h * 2000h, using 16-bit operands:
.data
val1 WORD 2000h val2 WORD 100h .code
mov ax,val1
mul val2 ; DX:AX = 00200000h, CF=1
The Carry flag
indicates whether or not the upper half of the product contains significant digits.
mov eax,12345h mov ebx,1000h
12345h * 1000h, using 32-bit operands:
Your turn . . . Your turn . . .
mov ax,1234h mov bx,100h mul bx
What will be the hexadecimal values of DX, AX, and the Carry flag after the following instructions execute?
DX = 0012h, AX = 3400h, CF = 1
Your turn . . . Your turn . . .
mov eax,00128765h mov ecx,10000h mul ecx
What will be the hexadecimal values of EDX, EAX, and the Carry flag after the following instructions execute?
EDX = 00000012h, EAX = 87650000h, CF = 1
IMUL Instruction IMUL Instruction
• IMUL (signed integer multiply ) multiplies an 8-, 16-, or 32-bit signed operand by either AL, AX, or EAX
• Preserves the sign of the product by sign-extending it into the upper half of the destination register
Example: multiply 48 * 4, using 8-bit operands:
mov al,48 mov bl,4
imul bl ; AX = 00C0h, OF=1
OF=1 because AH is not a sign extension of AL.
IMUL Examples IMUL Examples
Multiply 4,823,424 * −423:
mov eax,4823424 mov ebx,-423
imul ebx ; EDX:EAX = FFFFFFFF86635D80h, OF=0
OF=0 because EDX is a sign extension of EAX.
Your turn . . . Your turn . . .
mov ax,8760h mov bx,100h imul bx
What will be the hexadecimal values of DX, AX, and the Overflow flag after the following instructions execute?
DX = FF87h, AX = 6000h, OF = 1
DIV Instruction DIV Instruction
• The DIV (unsigned divide) instruction performs 8-bit, 16-bit, and 32-bit division on unsigned integers
• A single operand is supplied (register or memory operand), which is assumed to be the divisor
• Instruction formats:
DIV r/m8 DIV r/m16
DIV r/m32 Default Operands:
DIV Examples DIV Examples
Divide 8003h by 100h, using 16-bit operands:
mov dx,0 ; clear dividend, high mov ax,8003h ; dividend, low
mov cx,100h ; divisor
div cx ; AX = 0080h, DX = 3
Same division, using 32-bit operands:
mov edx,0 ; clear dividend, high mov eax,8003h ; dividend, low
mov ecx,100h ; divisor
div ecx ; EAX = 00000080h, EDX = 3
Your turn . . . Your turn . . .
mov dx,0087h mov ax,6000h mov bx,100h div bx
What will be the hexadecimal values of DX and AX after the following instructions execute? Or, if divide overflow occurs, you can indicate that as your answer:
DX = 0000h, AX = 8760h
Your turn . . . Your turn . . .
mov dx,0087h mov ax,6002h mov bx,10h div bx
What will be the hexadecimal values of DX and AX after the following instructions execute? Or, if divide overflow occurs, you can indicate that as your answer:
Divide Overflow
Signed Integer Division Signed Integer Division
• Signed integers must be sign-extended before division takes place
• fill high byte/word/doubleword with a copy of the low byte/word/doubleword's sign bit
• For example, the high byte contains a copy of the sign bit from the low byte:
1 0 0 0 1 1 1 1
1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
CBW, CWD, CDQ Instructions CBW, CWD, CDQ Instructions
• The CBW, CWD, and CDQ instructions
provide important sign-extension operations:
• CBW (convert byte to word) extends AL into AH
• CWD (convert word to doubleword) extends AX into DX
• CDQ (convert doubleword to quadword) extends EAX into EDX
• For example:
mov eax,0FFFFFF9Bh
cdq ; EDX:EAX = FFFFFFFFFFFFFF9Bh
IDIV Instruction IDIV Instruction
• IDIV (signed divide) performs signed integer division
• Uses same operands as DIV
Example: 8-bit division of –48 by 5
mov al,-48
cbw ; extend AL into AH mov bl,5
idiv bl ; AL = -9, AH = -3
IDIV Examples IDIV Examples
Example: 32-bit division of –48 by 5
mov eax,-48
cdq ; extend EAX into EDX mov ebx,5
idiv ebx ; EAX = -9, EDX = -3
Example: 16-bit division of –48 by 5
mov ax,-48
cwd ; extend AX into DX mov bx,5
idiv bx ; AX = -9, DX = -3
Implementing Arithmetic Expressions
Implementing Arithmetic Expressions
(1 of 3)(1 of 3)• Some good reasons to learn how to implement expressions:
• Learn how do compilers do it
• Test your understanding of MUL, IMUL, DIV, and IDIV
• Check for overflow
Example: var4 = (var1 + var2) * var3 mov eax,var1
add eax,var2 mul var3
jo TooBig ; check for overflow mov var4,eax ; save product
Implementing Arithmetic Expressions
Implementing Arithmetic Expressions
(2 of 3)(2 of 3)Example: eax = (-var1 * var2) + var3 mov eax,var1
neg eax mul var2
jo TooBig ; check for overflow add eax,var3
Example: var4 = (var1 * 5) / (var2 – 3) mov eax,var1 ; left side
mov ebx,5
mul ebx ; EDX:EAX = product mov ebx,var2 ; right side sub ebx,3
Implementing Arithmetic Expressions
Implementing Arithmetic Expressions
(3 of 3)(3 of 3)Example: var4 = (var1 * -5) / (-var2 % var3);
mov eax,var2 ; begin right side neg eax
cdq ; sign-extend dividend
idiv var3 ; EDX = remainder mov ebx,edx ; EBX = right side mov eax,-5 ; begin left side
imul var1 ; EDX:EAX = left side idiv ebx ; final division
mov var4,eax ; quotient
Your turn . . . Your turn . . .
mov eax,20 imul ebx idiv ecx
Implement the following expression using signed 32-bit integers:
eax = (ebx * 20) / ecx
Your turn . . . Your turn . . .
push ecx push edx
push eax ; EAX needed later mov eax,ecx
mul edx ; left side: EDX:EAX pop ecx ; saved value of EAX div ecx ; EAX = quotient
pop edx ; restore EDX, ECX pop ecx
Implement the following expression using unsigned 32- bit integers. Save and restore ECX and EDX:
eax = (ecx * edx) / ecx
Your turn . . . Your turn . . .
mov eax,var1 mov edx,var2 neg edx
imul edx ; left side: edx:eax mov ecx,var3
sub ecx,ebx
idiv ecx ; eax = quotient mov var3,eax
Implement the following expression using signed 32-bit integers. Do not modify any variables other than var3:
var3 = (var1 * -var2) / (var3 – ebx)
Extended ASCII Addition and Subtraction Extended ASCII Addition and Subtraction
• ADC Instruction
• Extended Addition Example
• SBB Instruction
ADC Instruction ADC Instruction
• ADC (add with carry) instruction adds both a source operand and the contents of the Carry flag to a
destination operand.
• Example: Add two 32-bit integers (FFFFFFFFh + FFFFFFFFh), producing a 64-bit sum:
mov edx,0
mov eax,0FFFFFFFFh add eax,0FFFFFFFFh
adc edx,0 ;EDX:EAX = 00000001FFFFFFFEh
Extended Addition Example Extended Addition Example
• Add two integers of any size
• Pass pointers to the addends and sum
• ECX indicates the number of doublewords
L1: mov eax,[esi] ; get the first integer adc eax,[edi] ; add the second integer pushfd ; save the Carry flag mov [ebx],eax ; store partial sum
add esi,4 ; advance all 3 pointers add edi,4
add ebx,4
popfd ; restore the Carry flag loop L1 ; repeat the loop
adc word ptr [ebx],0 ; add any leftover carry
SBB Instruction SBB Instruction
• The SBB (subtract with borrow) instruction subtracts both a source operand and the value of the Carry flag from a
destination operand.
• The following example code performs 64-bit subtraction. It sets EDX:EAX to 0000000100000000h and subtracts 1 from this value. The lower 32 bits are subtracted first, setting the Carry flag. Then the upper 32 bits are subtracted, including the Carry flag:
mov edx,1 ; upper half
mov eax,0 ; lower half
sub eax,1 ; subtract 1
sbb edx,0 ; subtract upper half
ASCII and Packed Decimal Arithmetic ASCII and Packed Decimal Arithmetic
• Unpacked BCD
• ASCII Decimal
• AAA Instruction
• AAS Instruction
• AAM Instruction
• AAD Instruction
• Packed Decimal Integers
• DAA Instruction
• DAS Instruction
Unpacked BCD Unpacked BCD
• Binary-coded decimal (BCD) numbers use 4 binary bits to represent each decimal digit
• A number using unpacked BCD representation stores a decimal digit in the lower four bits of each byte
• For example, 5,678 is stored as the following sequence of hexadecimal bytes:
05 06 07 08
ASCII Decimal ASCII Decimal
• A number using ASCII Decimal representation stores a single ASCII digit in each byte
• For example, 5,678 is stored as the following sequence of hexadecimal bytes:
35 36 37 38
AAA Instruction AAA Instruction
• The AAA (ASCII adjust after addition) instruction adjusts the binary result of an ADD or ADC
instruction. It makes the result in AL consistent with ASCII digit representation.
• The Carry value, if any ends up in AH
• Example: Add '8' and '2'
mov ah,0
mov al,'8' ; AX = 0038h add al,'2' ; AX = 006Ah
aaa ; AX = 0100h (adjust result) or ax,3030h ; AX = 3130h = '10'
AAS Instruction AAS Instruction
• The AAS (ASCII adjust after subtraction) instruction
adjusts the binary result of an SUB or SBB instruction. It makes the result in AL consistent with ASCII digit
representation.
• It places the Carry value, if any, in AH
• Example: Subtract '9' from '8'
mov ah,0
mov al,'8' ; AX = 0038h sub al,'9' ; AX = 00FFh
aas ; AX = FF09h (adjust result) pushf ; save Carry flag
or al,30h ; AX = FF39h (AL = '9')
AAM Instruction AAM Instruction
• The AAM (ASCII adjust after multiplication) instruction adjusts the binary result of a MUL instruction. The
multiplication must have been performed on unpacked decimal numbers.
mov bl,05h ; first operand mov al,06h ; second operand
mul bl ; AX = 001Eh
aam ; AX = 0300h
AAD Instruction AAD Instruction
• The AAD (ASCII adjust before division) instruction adjusts the unpacked decimal dividend in AX before a division operation
.data
quotient BYTE ? remainder BYTE ? .code
mov ax,0307h ; dividend
aad ; AX = 0025h
mov bl,5 ; divisor
div bl ; AX = 0207h
mov quotient,al mov remainder,ah
Packed Decimal Integers Packed Decimal Integers
• Packed BCD stores two decimal digits per byte
• For example, 12,345,678 can be stored as the following sequence of hexadecimal bytes:
12 34 56 78
DAA Instruction DAA Instruction
• The DAA (decimal adjust after addition) instruction converts the binary result of an ADD or ADC
operation to packed decimal format.
• The value to be adjusted must be in AL
• Example: calculate BCD 35 + 48
mov al,35h
add al,48h ; AL = 7Dh
daa ; AL = 83h (adjusted)
DAS Instruction DAS Instruction
• The DAS (decimal adjust after subtraction) instruction converts the binary result of a SUB or SBB operation to packed decimal format.
• The value must be in AL
• Example: subtract BCD 48 from 85
mov al,85h
sub al,48h ; AL = 3Dh
das ; AL = 37h (adjusted)