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Arithmetic and Logical Instructions

All of the two-operand arithmetic and logical instructions offer the same range of addressing modes. For example, here are the valid forms of the ADD operation:
        ADD     reg8, r/m/i8
        ADD     mem8, reg8
        ADD     mem8, BYTE imm8

        ADD     reg16, r/m/i16
        ADD     mem16, reg16
        ADD     mem16, WORD imm16
Just as with the MOV instruction, the first operand is the destination and the second is the source; the result of performing the operation on the two operands is stored in the destination (if it gets stored anywhere). Unlike MOV, most of these instructions also set or clear the appropriate status flags to reflect the result of the operation (for some of the instructions, this is their only effect).

To add two numbers, use the ADD instruction. To continue adding further bytes or words of a multi-part number, use the ADC instruction to also add one if the Carry flag is set (indicating a carry-over from the previous byte or word). For example, to add the 32-bit immediate value 12345678h to the 32-bit double word stored at location 500h, do ADD [500h], 5678h followed by ADC [502h], 1234h.

Subtraction is analogous: use the SUB instruction to subtract a single pair of bytes or words, and then use the SBB ("Subtract with Borrow'') instruction to take the Carry into account for further bytes or words.

An important use of subtraction is in comparing two numbers; in this case, we are not interested in the exact value of their difference, only in whether it is zero or negative, or whether there was a carry or overflow. The CMP ("Compare'') instruction performs this task; it subtracts the source from the destination and adjusts the status flags accordingly, but throws away the result. This is exactly what is needed to get conditions such as LE to work; after doing CMP AX, 10, for example, the status flags will be set in such a way that the LE condition is true precisely when the value in AX (treated as a signed integer) is less than or equal to 10.

The two-operand logical instructions are AND, OR, XOR, and TEST. The first three perform the expected bitwise operations; for example, the nth bit of the destination after the AND operation will be 1 (set, true) if the nth bit of both the source and the destination were 1 before the operation, otherwise it will be 0 (clear, false). The TEST instruction is to AND as CMP is to SUB; it performs a bitwise and operation, but the result is only reflected in the flags. For example, after the instruction TEST [321h], BYTE 12h, the Zero flag will be set if neither bit 1 nor bit 4 (12h is 00010010 in binary, indicating that bits 1 and 4 are to be tested) of the byte at address 321h were 1, otherwise it will be clear.

Multiplication and division are also binary operations, but the corresponding instructions on the 8086 only allow one of the operands to be specified (and it can only be a register or memory reference, not an immediate value). The other operand is implicitly contained in the accumulator (and sometimes also the DX register). The MUL and DIV instructions operate on unsigned numbers, while IMUL and IDIV operate on two's-complement signed numbers. Here are the valid forms for MUL; the others are analogous:

        MUL     reg8
        MUL     BYTE mem8

        MUL     reg16
        MUL     WORD mem16
For 8-bit multiplication, the quantity in AL is multiplied by the given operand and the 16-bit result is placed in AX. For 16-bit multiplication, the 32-bit product of AX and the operand is split, with the low word in AX and the high word in DX. In both cases, if the result spills into the high-order byte/word, then the Carry and Overflow flags will be set, otherwise they will be clear. The other flags will have garbage in them; in particular, you will not get correct information from the Zero or Sign flags (if you want that information, follow the multiplication with CMP AX, 0, for example).

For division, the process is reversed. An 8-bit operand will be divided into the number in AX, with the quotient stored in AL and the remainder left in AH. A 16-bit operand will be divided into the 32-bit quantity whose high word is in DX and whose low word is in AX; the quotient will be in AX and the remainder will be in DX after the operation. None of the status flags are defined after a division. Also, if the division results in an error (division by zero, or a quotient that is too large), the processor will trigger interrupt zero (as if it had executed INT 0).

The CBW and CWD instructions, which take no operands, will sign-extend AL into AX or AX into DX, respectively, just as needed before performing a signed division. For example, if AL contains 11010110, then after CBW the AH register will contain 11111111 (and AL will be unchanged).

Multiplication and division by powers of two are frequently performed by shifting the bits to the left or right. There are several varieties of shift and rotate instructions, all of which allow the following forms:

        RCL     reg8, 1
        RCL     reg8, CL
        RCL     BYTE mem8, 1
        RCL     BYTE mem8, CL

        RCL     reg16, 1
        RCL     reg16, CL
        RCL     WORD mem16, 1
        RCL     WORD mem16, CL
The second operand specifies how many bit positions the result should be shifted by: either one or the number in the CL register. For example, the accumulator may be multiplied by 2 with SHL AX, 1; if CL contains the number 4, the accumulator may be multiplied by 16 with SHL AX, CL.

There are three shift instructions---SAR, SHR, and SHL. The "shift-left'' instruction, SHL, shifts the highest bit of the operand into the Carry flag and fills in the lowest bit with zero. The "shift-right'' instruction, SHR, does the opposite, moving zero in from the top and shifting the lowest bit out into the Carry; this is appropriate for an unsigned division, with the Carry flag giving a 1-bit remainder. On the other hand, the "shift-arithmetic-right'' instruction, SAR, leaves a copy of the highest bit in place as it shifts; this is appropriate for a signed division, since it preserves the sign bit.

For example, -53 is represented in 8-bit two's-complement by the binary number 11001011. After a SHL by one position, it will be 10010110, which represents -106. After a SAR, it will be 11100101, which represents -27. After a SHR, it will be 01100101, which represents +101 in decimal; this corresponds to the interpretation of the original bits as the unsigned number 203 (which yields 101 when divided by 2).

When shifting multiple words by one bit, the Carry can serve as the bridge from one word to the next. For example, suppose we want to multiply the double word (4 bytes) starting at address 1230h by 2; the instruction SHL WORD [1230], 1 will shift the low-order word, putting its highest bit into the Carry flag. Now we need an instruction that will shift the Carry into the lowest bit of the word at 1232h; if we wanted to continue the process, we would also need it to shift the highest bit of that word back out into the Carry. The effect here is that the bits in the operand plus the Carry have been rotated one position to the left. The desired instruction is RCL WORD [1232], 1 ("rotate-carry-left''). There is a corresponding "rotate-carry-right'' instruction, RCR; there are also two rotate instructions which directly shift the highest bit down to the lowest and vice versa, called ROL and ROR.

There are four unary arithmetic and logical instructions. The increment and decrement operations, INC and DEC, add or subtract one from their operand; they do not affect the Carry bit. The negation instruction, NEG, takes the two's-complement of its operand, while the NOT instruction takes the one's-complement (flip each bit from 1 to 0 or 0 to 1). NEG affects all the usual flags, but NOT does not affect any of them. The valid forms of operand are the same for all of these instructions; here are the forms for INC:

        INC     reg8
        INC     BYTE mem8

        INC     reg16
        INC     WORD mem16