COMPARISON AND CONDITIONS

Conditional jump was introduced in the last chapter to loop for the addition of a fixed number of array elements. The jump was based on the zero flag. There are many other conditions possible in a program. For example an operand can be greater than another operand or it can be smaller. We use comparisons and boolean expressions extensively in higher level languages. They must be available is some form in assembly language, otherwise they could not possibly be made available in a higher level language. In fact they are available in a very fi ne and purified form.

The basic root instruction for all comparisons is CMP standing for compare. The operation of CMP is to subtract the source operand from the destination operand, updating the flags without changing either the source or the destination. CMP is one of the key instructions as it introduces the capability of conditional routing in the processor.

A closer thought reveals that with subtraction we can check many different conditions. For example if a larger number is subtracted from a smaller number a borrow is needed. The carry flag plays the role of borrow during the subtraction operation. And in this condition the carry flag will be set. If two equal numbers are subtracted the answer is zero and the zero flag will be set. Every significant relation between the destination and source is evident from the sign flag, carry flag, zero flag, and the overflow flag. CMP is meaningless without a conditional jump immediately following it.

Another important distinction at this point is the difference between signed and unsigned numbers. In unsigned numbers only the magnitude of the number is important, whereas in signed numbers both the magnitude and the sign are important. For example -2 is greater than -3 but 2 is smaller than 3. The sign has affected our comparisons.

Inside the computer signed numbers are represented in two’s complement notation. In essence a number in this representation is still a number, just that now our interpretation of this number will be signed. Whether we use jump above and below or we use jump greater or less will convey our intention to the processor. The jump above and greater operations at first sight seem to be doing the same operation, and similarly below and less operations seem to be similar. However for signed numbers JG and JL will work properly and for unsigned JA and JB will work properly and not the other way around.

It is important to note that at the time of comparison, the intent of the programmer to treat the numbers as signed or unsigned is not clear. The subtraction in CMP is a normal subtraction. It is only after the comparison, during the conditional jump operation, that the intent is conveyed. At that time with a specific combination of flags checked the intent is satisfied.

For example a number 2 is represented in a word as 0002 while the number -2 is represented as FFFE. In a byte they would be represented as 02 and FE. Now both have the same magnitude however the different sign has caused very different representation in two’s complement form. Now if the intent is to use FFFE or decimal 65534 then the same data would be placed in the word as in case of -2. In fact if -2 and 65534 are compared the processor will set the zero flag signaling that they are exactly equal. As regards an unsigned comparison the number 65534 is much greater than 2.

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So if a JA is taken after comparing -2 in the destination with 2 in the source the jump will be taken. If however JG is used after the same comparison the jump will not be taken as it will consider the sign and with the sign -2 is smaller than 2. The key idea is that -2 and 65534 were both stored in memory in the same form. It was the interpretation that treated it as a signed or as an unsigned number.

The unsigned comparisons see the numbers as 0 being the smallest and 65535 being the largest with the order that 0 < 1 < 2 … < 65535. The signed comparisons see the number -32768 which has the same memory representation as 32768 as the smallest number and 32767 as the largest with the order -32768 < -32767 < … < -1 < 0 < 1 < 2 < … < 32767. All the negative numbers have the same representation as an unsigned number in the range 32768 … 65535 however the signed interpretation of the signed comparisons makes them be treated as negative numbers smaller than zero.

All meaningful situations both for signed and unsigned numbers than occur after a comparison are detailed in the following table.

DEST = SRC ZF = 1 When the source is subtracted
from the destination and both are
equal the result is zero and
therefore the zero flag is set. This
works for both signed and
unsigned numbers.

UDEST < USRC CF = 1 When an unsigned source is
subtracted from an unsigned
destination and the destination is
smaller, a borrow is needed
which sets the carry flag.

UDEST  USRC ZF = 1 OR CF = 1 If the zero flag is set, it means
that the source and destination
are equal and if the carry flag is
set it means a borrow was needed
in the subtraction and therefore
the destination is smaller.

UDEST  USRC CF = 0 When an unsigned source is
subtracted from an unsigned
destination no borrow will be
needed either when the operands
are equal or when the destination
is greater than the source.

UDEST > USRC ZF = 0 AND CF = 0 The unsigned source and
destination are not equal if the
zero flag is not set and the
destination is not smaller since
no borrow was taken. Therefore
the destination is greater than
the source.

SDEST < SSRC SF  OF When a signed source is
subtracted from a signed
destination and the answer is
negative with no overflow than
the destination is smaller than
the source. If however there is an
overflow meaning that the sign
has changed unexpectedly, the
meanings are reversed and a


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positive number signals that the
destination is smaller.

SDEST  SSRC ZF = 1 OR SF  OF If the zero flag is set, it means
that the source and destination
are equal and if the sign and
overflow flags differ it means that
the destination is smaller as
described above.

SDEST  SSRC SF = OF When a signed source is
subtracted from a signed
destination and the answer is
positive with no overflow than the
destination is greater than the
source. When an overflow is there
signaling that sign has changed
unexpectedly, we interpret a
negative answer as the signal
that the destination is greater.

SDEST > SSRC ZF = 0 AND SF = OF If the zero flag is not set, it means
that the signed operands are not
equal and if the sign and overflow
match in addition to this it
means that the destination is
greater than the source.