Integer Multiplication and Division

1
Integer Multiplication and Division

• Assembly Language Programming
• University of Akron
• Dr. Tim Margush

2
Multiply Instruction

• Signed Multiply
• IMUL source
• Unsigned Multiply
• MUL source
• source can be a register or memory location (not
  a constant)

• Byte form
• AXALsource
• Word form
• DXAXAXsource
• CFOF
• 1 if answer size gt op size
• 0 otherwise
• SF, ZF, AF, and PF
• Undefined

3
IMUL Example

• mov BL,0FEh
• mov AL,0E5h
• imul BL
• BL contains -2, AL contains -27
• After IMUL
• AX contains 0036h (54d)
• CFOF0 (result still fits in byte)
• SF, AF, PF, and ZF are undefined

4
MUL Example

• mov BL,0FEh
• mov AL,0E5h
• mul BL
• BL contains 254, AL contains 229
• After MUL
• AX contains 0E336h (58166d)
• CFOF1 (result requires a word)
• SF, AF, PF, and ZF are undefined

5
Another IMUL Example

• mov AWORD,-136
• mov AX,6784
• imul AWORD
• AWORD contains 0FF78h, AX is 1A80h
• After IMUL
• DXAX contains 0FFF1EC00h (-922624d)
• CFOF1 (result requires a doubleword)

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Another MUL Example

• mov AWORD,-136
• mov AX,6784
• mul AWORD
• AWORD is 0FF78h (65400d), AX is 1A80h
• After MUL
• DXAX contains 1A71EC00h (443673600d)
• CFOF1 (result requires a doubleword)

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One More IMUL Example

• mov AX,-1
• mov DX,2
• imul DX
• AX is 0FFFFh, BX is 0002h
• After IMUL
• DXAX contains 0FFFFFFFEh (-2d)
• CFOF0 (result still fits in a word)

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Application Formatted Decimal Input

• Input a number (sequence of decimal digits)
• Implement as a procedure
• Skip leading whitespace, stop processing at next
  whitespace (tab, space, or newline)
• Return result in AX
• Return with CF1 if error occurred
• Errors overflow, illegal digit, no digit
• Assume unsigned data for this example

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Conversion Algorithm

• skip whitespace
• v 0
• while (digit d is not whitespace)
• if (illegal) set illegal flag
• otherwise process digit
• v v10 d
• if (overflow) set overflow flag

• nextDigit
• mov ax,10
• mul valueSoFar
• jo setOF
• add ax,digitValue
• jnc nextDigit
• setOF incOFFlag
• jmp nextDigit

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Divide Instruction

• Signed Divide
• IDIV divisor
• Unsigned Divide
• DIV divisor
• divisor can be a register or memory location (not
  a constant)

• Byte form
• ALAX / divisor
• AHAX divisor
• Word form
• AXDXAX / divisor
• DXDXAX divisor
• All Flags undefined
• For IDIV
• sign of dividend sign of remainder

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Divide Overflow

• Occurs when result will not fit in Word/Byte
• Terminates program with Divide Overflow message!
• Need to anticipate and avoid It will occur if
• Byte form AHgtdivisor
• Word form DXgtdivisor

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Preparing Dividend

• To divide a word in AX by a word, AX must be
  converted to a doubleword in DXAX
• If signed CWD (called sign-extension)
• If unsigned MOV DX,0
• For byte (in AL) to word (AX) conversion
• If signed CBW (these do not affect Flags)
• If unsigned MOV AH,0

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Formatted Numeric Output

• Want to produce a sequence of characters
  representing a number in some representation
  scheme
• decimal, hex, octal, binary are common
  representation schemes
• decimal format usually implies a sign might be
  shown if the number is negative (assuming we are
  displaying a signed value)

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Generating the Digits

• least_significant_digit value base
• we can reuse this computation for the next digit
  if we modify value value value / base
• The process repeats until a 0 is obtained or the
  desired number of digits determined
• Problem we generate the digits in the wrong
  order for display

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Reversing the Digits

• Solution A
• Push digits on stack as they are discovered
• Pop each digit off the stack and display it

• Solution B
• Store digits in an array as they are discovered
• Display digits from the array in the opposite
  order

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A Decimal Output Procedure

• Given an unsigned number in AX, fill character in
  DH and field width in DL
• Display the decimal representation on the screen,
  right justified in the specified field with the
  specified fill character
• If DL is smaller than the required number of
  digits, display all digits of the result, no fill)

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DECOUT Procedure

• decout proc near
• Output AX in decimal format
• DH fill char, DL field width
• count and push ASCII code of the
• significant digits onto the stack
• display fill characters if needed
• display digits from stack
• ret
• decout endp

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Homework

• Pg 176
• parts a, b, and c only of 1, 2, 3, 4
• 5, 6, and 7b