About this Lecture

• Logical Operations
• Shifting Operations
• Math Operations
• Overflows and Carries
• Flag Settings
• Using the flags for program branching
• Using the flags for math operations

Family of Logical Operations

Family of Shifting Operations

• Single-bit shifting

  

• SHL == SAL : Shift Left (insert zero)
  (Also: A quick way to double a number as well!)
• SHR : Shift Right (insert zero)
  (Also: A quick way to divide by two!)
• SAR : Shift Arithmetic Right (preserve high-bit)
  (Also: A quick way to divide by two!)
• ROL : Rotate Left
• RCL : use 9th/17th carry flag
• ROR : Rotate Right
• RCR : use 9th/17th carry flag
• Note: Carry flag (CF) always receives the shifted-out result
• Note: Register CL can be used for shifts > 1 bit.

• Examples

Family of Simple Math Operations

• ADD : Add : A+=B
• SUB : Subtract : A-=B
• NEG : A=-A
• INC : A++ (Does not affect carry flag)
• DEC : A-- (Does not affect carry flag)

Overflows and Carries

• When we add or subtract large numbers, we may carry or overflow

• Recall that the word size dictates the range of the elements
  • 1 Byte unsigned integer: 0 .. 255 (0 .. 2^8-1)

  • 1 Byte signed integer: -128 .. 127 (-2^7 .. 2^7-1)

  • 2 Byte unsigned integer: 0 .. 65535 (0 .. 2^16-1)

  • 2 Byte signed integer: -32768 .. 32767 (-2^15 .. 2^15-1)

  • 4 Byte unsigned integer: 0 .. 4.2 Billion (0 .. 2^32-1)
    (This is roughly the population of the earth)
    (IP addresses use 4 bytes)

  • 4 Byte signed integer: -2.1 Billion .. 2.1 Billion-1 (about) (-2^31 .. 2+31-1)

• Results may change the 9th/17th bit (for 8-bit/16-bit operations)

• CF: Carry Flag (unsigned) = {1=CY , 0=NC}
  eg: 36,864 (9000H) + 36,864 (9000H) = 73,728 (12000H) > 65,535 (FFFFH) : OV,CY
  Carry is set when unsigned goes out of range.

• OF: Overflow Flag (signed) = {1=OV , 0=NV}
  eg: 20,480 (5000H) + 20,480 (5000H) = 40,960 (A000H) > 32,767 (7FFFH) : OV,NC
  Overflow is set when signed goes out of range.

• Example
• Other examples
  • 8000H+2000H=A000H :NV,NC (-)+(+) cannot overflow!
  • FFFFH+FFFFH=FFFEH :NV,CY (-1)+(-1)=(-2)

Flag Settings

• (first mentioned as a register in lecture 2)

• Flag	Name	Description	Notes
  ZF	Zero Flag	1:ZR:Zero 0:NZ:Non-zero	1 indicates that the result was zero!
  CF	Carry Flag	1:CY 0:NC	Unsigned math and shifting Needed a carry or borrow.
  OF	Overflow Flag	1:OV 0:NV	Signed Math Too (+) or (-) to be represented as a valid 2's complement number
  SF	Sign Flag	1:NG:- 0:PL:+	MSB of result

• Modified by logical and mathematical operations
• The CPU sets the flags after the operation to tell you about the result (as you would expect)

Using the Flags for math operations

• ADC Add with carry (add CF to result) : Operate on LSBs first!

• SBB Sub with borrow (subtract CF from result) : Operate on LSBs first!

Using the Flags for program branching

• Flags retain state information from previous instruction(s).
• Conditional jump commands read the flags to transfer program execution elsewhere, based on the value of the flags and the content of the registers.

• CMP : Same as SUB, but does not write result (only sets flags)
  i.e., CMP A,B performs A-B
  eg: CMP 5,4 performs 5-4=1 : NZ PL NC NV

• 80x86 conditional jumps (JE,JL,JG,JNE,etc..) are short jumps (signed, 8-bit displacement).
• JMP: (Unconditional JUMP) allows long displacement