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Assembly Language Programming

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3.1. 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 fine 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 then 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, borrow is needed which
sets the carry flag.
ZF = 1 OR CF = 1
If the zero flag is set, it means
UDEST USRC
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.
CF = 0
When an unsigned source  is
UDEST USRC
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
When  a  signed  source  is
SF OF
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.
If the zero flag is set, it means
SDEST SSRC
ZF = 1 OR SF OF
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.
SF = OF
When  a  signed  source  is
SDEST SSRC
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.
3.2. CONDITIONAL JUMPS
For every interesting or meaningful situation of flags, a conditional jump is
there. For example JZ and JNZ check the zero flag. If in a comparison both
operands are same, the result of subtraction will be zero and the zero flag
will be set. Thus JZ and JNZ can be used to test equality. That is why there
are renamed versions JE and JNE read as jump if equal or jump if not equal.
They seem more logical in writing but mean exactly the same thing with the
same opcode. Many jumps are renamed with two or three names for the
same jump, so that the appropriate logic can be conveyed in assembly
language programs. This renaming is done by Intel and is a standard for
iAPX88. JC and JNC test the carry flag. For example we may need to test
whether there was an overflow in the last unsigned addition or subtraction.
Carry flag will also be set if two unsigned numbers are subtracted and the
first is smaller than the second. Therefore the renamed versions JB, JNAE,
and JNB, JAE are there standing for jump if below, jump if not above or
equal, jump if not below, and jump if above or equal respectively. The
operation of all jumps can be seen from the following table.
JC
Jump if carry
CF = 1
This jump is taken if
JB
Jump if below
the  last  arithmetic
JNAE
Jump if not above or equal
operation generated a
carry or required a
borrow. After a CMP it
is
taken
if
the
unsigned  source  is
smaller
than
the
unsigned destination.
JNC
Jump if not carry
CF = 0
This jump is taken if
JNB
Jump if not below
the  last  arithmetic
JAE
Jump if above or equal
operation
did
not
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generated a carry or
required  a  borrow.
After a CMP it is taken
if the unsigned source
is larger or equal to
the
unsigned
destination.
JE
Jump if equal
ZF = 1
This jump is taken if
JZ
Jump if zero
the  last  arithmetic
operation produced a
zero in its destination.
After a CMP it is taken
if both operands were
equal.
JNE
Jump if not equal
ZF = 0
This jump is taken if
JNZ
Jump if not zero
the  last  arithmetic
operation
did
not
produce a zero in its
destination.  After  a
CMP it is taken if both
operands
were
different.
JA
Jump if above
ZF = 0 AND
This jump is taken
JNBE
Jump if not below or equal
CF = 0
after a CMP if the
unsigned  source  is
larger
than
the
unsigned destination.
JNA
Jump if not above
ZF = 1 OR
This jump is taken
JBE
Jump if not below or equal
CF = 1
after a CMP if the
unsigned  source  is
smaller than or equal
to
the
unsigned
destination.
This jump is taken
JL
Jump if less
SF OF
after a CMP if the
JNGE
Jump if not greater or equal
signed
source
is
smaller
than
the
signed destination.
JNL
Jump if not less
SF = OF
This jump is taken
JGE
Jump if greater or equal
after a CMP if the
signed source is larger
than or equal to the
signed destination.
JG
Jump if greater
ZF = 0 AND
This jump is taken
JNLE
Jump if not less or equal
SF = OF
after a CMP if the
signed source is larger
than
the
signed
destination.
JNG
Jump if not greater
ZF = 1 OR
This jump is taken
JLE
Jump if less or equal
after a CMP if the
SF OF
signed
source
is
smaller than or equal
to
the
signed
destination.
34
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JO
Jump if overflow.
OF = 1
This jump is taken if
the  last  arithmetic
operation changed the
sign unexpectedly.
JNO
Jump if not overflow
OF = 0
This jump is taken if
the  last  arithmetic
operation
did
not
change
the
sign
unexpectedly.
JS
Jump if sign
SF = 1
This jump is taken if
the  last  arithmetic
operation produced a
negative number in its
destination.
JNS
Jump if not sign
SF = 0
This jump is taken if
the  last  arithmetic
operation produced a
positive number in its
destination.
JP
Jump if parity
PF = 1
This jump is taken if
JPE
Jump if even parity
the  last  arithmetic
operation produced a
number
in
its
destination that has
even parity.
JNP
Jump if not parity
PF = 0
This jump is taken if
JPO
Jump if odd parity
the  last  arithmetic
operation produced a
number
in
its
destination that has
odd parity.
JCXZ
Jump if CX is zero
CX = 0
This jump is taken if
the CX register is zero.
The CMP instruction sets the flags reflecting the relation of the destination
to the source. This is important as when we say jump if above, then what is
above what. The destination is above the source or the source is above the
destination.
The JA and JB instructions are related to unsigned numbers. That is our
interpretation for the destination and source operands is unsigned. The 16th
bit holds data and not the sign. In the JL and JG instructions standing for
jump if lower and jump if greater respectively, the interpretation is signed.
The 16th bit holds the sign and not the data. The difference between them
will be made clear as an elaborate example will be given to explain the
difference.
One jump is special that it is not dependant on any flag. It is JCXZ, jump
if the CS register is zero. This is because of the special treatment of the CX
register as a counter. This jump is regardless of the zero flag. There is no
counterpart or not form of this instruction.
The adding numbers example of the last chapter can be a little simplified
using the compare instruction on the BX register and eliminating the need
for a separate counter as below.
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Computer Architecture & Assembly Language Programming
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Example 3.1
001
; a program to add ten numbers without a separate counter
002
[org 0x0100]
003
mov  bx, 0
; initialize array index to zero
004
mov  ax, 0
; initialize sum to zero
005
006
l1:
add
ax, [num1+bx]
;
add number to ax
007
add
bx, 2
;
advance bx to next index
008
cmp
bx, 20
;
are we beyond the last index
009
jne
l1
;
if not add next number
010
011
mov
[total], ax
; write back sum in memory
012
013
mov
ax, 0x4c00
; terminate program
014
int
0x21
015
016
num1:
dw
10, 20, 30, 40, 50, 10, 20, 30, 40, 50
017
total:
dw
0
The format of memory access is still base + offset.
006
BX is used as the array index as well as the counter. The offset of
008
11th number will be 20, so as soon as BX becomes 20 just after the
10th number has been added, the addition is stopped.
The jump is displayed as JNZ in the debugger even though we have
009
written JNE in our example. This is because it is a renamed jump
with the same opcode as JNZ and the debugger has no way of
knowing the mnemonic that we used after looking just at the
opcode. Also every code and data reference that we used till now is
seen in the opcode as well. However for the jump instruction we see
an operand of F2 in the opcode and not 0116. This will be discussed
in detail with unconditional jumps. It is actually a short relative
jump and the operand is stored in the form of positive or negative
offset from this instruction.
With conditional branching in hand, there are just a few small things left
in assembly language that fills some gaps. Now there is just imagination and
the skill to conceive programs that can make you write any program.
3.3. UNCONDITIONAL JUMP
Till now we have been placing data at the end of code. There is no such
restriction and we can define data anywhere in the code. Taking the previous
example, if we place data at the start of code instead of at the end and we
load our program in the debugger. We can see our data placed at the start
but the debugger is intending to start execution at our data. The COM file
definition said that the first executable instruction is at offset 0100 but we
have placed data there instead of code. So the debugger will try to interpret
that data as code and showed whatever it could make up out of those
opcodes.
We introduce a new instruction called JMP. It is the unconditional jump
that executes regardless of the state of all flags. So we write an unconditional
jump as the very first instruction of our program and jump to the next
instruction that follows our data declarations. This time 0100 contains a
valid first instruction of our program.
Example 3.2
001
; a program to add ten numbers without a separate counter
002
[org 0x0100]
003
jmp start
; unconditionally jump over data
004
005
num1:
dw
10, 20, 30, 40, 50, 10, 20, 30, 40, 50
006
total:
dw
0
36
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007
008
start:
mov
bx, 0
; initialize array index to zero
009
mov
ax, 0
; initialize sum to zero
010
011
l1:
add
ax, [num1+bx]
;
add number to ax
012
add
bx, 2
;
advance bx to next index
013
cmp
bx, 20
;
are we beyond the last index
014
jne
l1
;
if not add next number
015
016
mov
[total], ax
; write back sum in memory
017
018
mov
ax, 0x4c00
; terminate program
019
int
0x21
JMP jumps over the data declarations to the start label and
003
execution resumes from there.
3.4. RELATIVE ADDRESSING
Inside the debugger the instruction is shown as JMP 0119 and the location
0119 contains the original first instruction of the logic of our program. This
jump is unconditional, it will always be taken. Now looking at the opcode we
see F21600 where F2 is the opcode and 1600 is the operand to it. 1600 is
0016 in proper word order. 0119 is not given as a parameter rather 0016 is
given.
This is position relative addressing in contrast to absolute addressing. It is
not telling the exact address rather it is telling how much forward or
backward to go from the current position of IP in the current code segment.
So the instruction means to add 0016 to the IP register. At the time of
execution of the first instruction at 0100 IP was pointing to the next
instruction at 0103, so after adding 16 it became 0119, the desired target
location. The mechanism is important to know, however all calculations in
this mechanism are done by the assembler and by the processor. We just use
a label with the JMP instruction and are ensured that the instruction at the
target label will be the one to be executed.
3.5. TYPES OF JUMP
The three types of jump, near, short, and far, differ in the size of
instruction and the range of memory they can jump to with the smallest
short form of two bytes and a range of just 256 bytes to the far form of five
bytes and a range covering the whole memory.
Short Jump
Disp
EB
Near Jump
EB
Disp Low
Disp High
Far Jump
EB
IP Low
IP High
CS Low
CS High
Near Jump
When the relative address stored with the instruction is in 16 bits as in the
last example the jump is called a near jump. Using a near jump we can jump
anywhere within a segment. If we add a large number it will wrap around to
37
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the lower part. A negative number actually is a large number and works this
way using the wraparound behavior.
Short Jump
If the offset is stored in a single byte as in 75F2 with the opcode 75 and
operand F2, the jump is called a short jump. F2 is added to IP as a signed
byte. If the byte is negative the complement is negated from IP otherwise the
byte is added. Unconditional jumps can be short, near, and far. The far type
is yet to be discussed. Conditional jumps can only be short. A short jump
can go +127 bytes ahead in code and -128 bytes backwards and no more.
This is the limitation of a byte in singed representation.
Far Jump
Far jump is not position relative but is absolute. Both segment and offset
must be given to a far jump. The previous two jumps were used to jump
within a segment. Sometimes we may need to go from one code segment to
another, and near and short jumps cannot take us there. Far jump must be
used and a two byte segment and a two byte offset are given to it. It loads CS
wit the segment part and IP with the offset part. Execution therefore resumes
from that location in physical memory. The three instructions that have a far
form are JMP, CALL, and RET, are related to program control. Far capability
makes intra segment control possible.
3.6. SORTING EXAMPLE
Moving ahead from our example of adding numbers we progress to a
program that can sort a list of numbers using the tools that we have
accumulated till now. Sorting can be ascending or descending like if the
largest number comes at the top, followed by a smaller number and so on till
the smallest number the sort will be called descending. The other order
starting with the smallest number and ending at the largest is called
ascending sort. This is a common problem and many algorithms have been
developed to solve it. One simple algorithm is the bubble sort algorithm.
In this algorithm we compare consecutive numbers. If they are in required
order e.g. if it is a descending sort and the first is larger then the second,
then we leave them as it is and if they are not in order, we swap them. Then
we do the same process for the next two numbers and so on till the last two
are compared and possibly swapped.
A complete iteration is called a pass over the array. We need N passes at
least in the simplest algorithm if N is the number of elements to be sorted. A
finer algorithm is to check if any swap was done in this pass and stop as
soon as a pass goes without a swap. The array is now sorted as every pair of
elements is in order.
For example if our list of numbers is 60, 55, 45, and 58 and we want to
sort them in ascending order, the first comparison will be of 60 and 55 and
as the order will be reversed to 55 and 60. The next comparison will be of 60
and 45 and again the two will be swapped. The next comparison of 60 and 58
will also cause a swap. At the end of first pass the numbers will be in order
of 55, 45, 58, and 60. Observe that the largest number has bubbled down to
the bottom. Just like a bubble at bottom of water. In the next pass 55 and 45
will be swapped. 55 and 58 will not be swapped and 58 and 60 will also not
be swapped. In the next pass there will be no swap as the elements are in
order i.e. 45, 55, 58, and 60. The passes will be stopped as the last pass did
not cause any swap. The application of bubble sort on these numbers is
further explained with the following illustration.
38
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State of Data
Swap Done
Swap Flag
Pass 1
Off
Yes
On
60
55
45
58
Yes
On
55
60
45
58
Yes
On
55
45
60
58
Pass 2
Off
Yes
On
55
45
58
60
No
On
45
55
58
60
No
On
45
55
58
60
Pass 3
Off
No
Off
45
55
58
60
No
Off
45
55
58
60
No
Off
45
55
58
60
No more passes since swap flag is Off
Example 3.3
001
; sorting a list of ten numbers using bubble sort
002
[org 0x0100]
003
jmp  start
004
005
data:
dw
60, 55, 45, 50, 40, 35, 25, 30, 10, 0
006
swap:
db
0
007
008
start:
mov
bx, 0
; initialize array index to zero
009
mov
byte [swap], 0
; rest swap flag to no swaps
010
011
loop1:
mov
ax, [data+bx]
; load number in ax
012
cmp
ax, [data+bx+2]
; compare with next number
013
jbe
noswap
; no swap if already in order
014
015
mov
dx, [data+bx+2]
;
load second element in dx
016
mov
[data+bx+2], ax
;
store first number in second
017
mov
[data+bx], dx
;
store second number in first
018
mov
byte [swap], 1
;
flag that a swap has been done
019
020
noswap:
add
bx, 2
; advance bx to next index
021
cmp
bx, 18
; are we at last index
022
jne
loop1
; if not compare next two
023
024
cmp
byte [swap], 1
; check if a swap has been done
025
je
bsort
; if yes make another pass
026
027
mov
ax, 0x4c00
; terminate program
028
int
0x21
39
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The jump instruction is placed to skip over data.
003
The swap flag can be stored in a register but as an example it is
006
stored in memory and also to extend the concept at a later stage.
One element is read in AX and it is compared with the next element
011-012
because memory to memory comparisons are not allowed.
If the JBE is changed to JB, not only the unnecessary swap on equal
013
will be performed, there will be a major algorithmic flaw due to a
logical error as in the case of equal elements the algorithm will never
stop. JBE won't swap in the case of equal elements.
The swap is done using DX and AX registers in such a way that the
015-017
values are crossed. The code uses the information that one of the
elements is already in the AX register.
This time BX is compared with 18 instead of 20 even though the
021
number of elements is same. This is because we pick an element
and compare it with the next element. When we pick the 9th element
we compare it with the next element and this is the last comparison,
since if we pick the 10th element we will compare it with the 11th
element and there is no 11th element in our case.
If a swap is done we repeat the whole process for possible more
024-025
swaps.
Inside the debugger we observe that the JBE is changed to JNA due to the
same reason as discussed for JNE and JNZ. The passes change the data in
the same manner as we presented in our illustration above. If JBE in the
code is changed to JAE the sort will change from ascending to descending.
For signed numbers we can use JLE and JGE respectively for ascending and
descending sort.
To clarify the difference of signed and unsigned jumps we change the data
array in the last program to include some negative numbers as well. When
JBE will be used on this data, i.e. with unsigned interpretation of the data
and an ascending sort, the negative numbers will come at the end after the
largest positive number. However JLE will bring the negative numbers at the
very start of the list to bring them in proper ascending order according to a
signed interpretation, even though they are large in magnitude. The data
used is shown as below.
data:
dw 60, 55, 45, 50, -40, -35, 25, 30, 10, 0
This data includes some signed numbers as well. The JBE instruction will
treat this data as an unsigned number and will cater only for the magnitude
ignoring the sign. If the program is loaded in the debugger, the numbers will
appear in their hexadecimal equivalent. The two numbers -40 and -35 are
especially important as they are represented as FFD8 and FFDD. This data is
not telling whether it is signed or unsigned. Our interpretation will decide
whether it is a very large unsigned number or a signed number in two's
complement form.
If the sorting algorithm is applied on the above data with JBE as the
comparison  instruction  to  sort  in  ascending  order  with  unsigned
interpretation, observe the comparisons of the two numbers FFD8 and
FFDD. For example it will decide that FFDD > FFD8 since the first is larger
in magnitude. At the end of sorting FFDD will be at the end of the list being
declared the largest number and FFD8 will precede it to be the second
largest.
If however the comparison instruction is changed to JLE and sorting is
done on the same data it works similarly except on the two numbers FFDD
and FFD8. This time JLE declares them to be smaller than every other
number and also declares FFDD < FFD8. At the end of sorting, FFDD is
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declared to be the smallest number followed by FFD8 and then 0000. This is
in contrast to the last example where JBE was used. This happened because
JLE interpreted our data as signed numbers, and as a signed number FFDD
has its sign bit on signaling that it is a negative number in two's complement
form which is smaller than 0000 and every positive number. However JBE
did not give any significance to the sign bit and included it in the magnitude.
Therefore it declared the negative numbers to be the largest numbers.
If the required interpretation was of signed numbers the result produced
by JLE is correct and if the required interpretation was of unsigned numbers
the result produced by JBE is correct. This is the very difference between
signed and unsigned integers in higher level languages, where the compiler
takes the responsibility of making the appropriate jump depending on the
type of integer used. But it is only at this level that we can understand the
actual mechanism going on. In assembly language, use of proper jump is the
responsibility of the programmer, to convey the intentions to use the data as
signed or as unsigned.
The remaining possibilities of signed descending sort and unsigned
descending sort can be done on the same lines and are left as an exercise.
Other conditional jumps work in the same manner and can be studied from
the reference at the end. Several will be discussed in more detail when they
are used in subsequent chapters.
EXERCISES
1. Which registers are changed by the CMP instruction?
2. What are the different types of jumps available? Describe position
relative addressing.
3. If AX=8FFF and BX=0FFF and "cmp ax, bx" is executed, which of the
following jumps will be taken? Each part is independent of others. Also
give the value of Z, S, and C flags.
a. jg greater
b. jl smaller
c. ja above
d. jb below
4. Write a program to find the maximum number and the minimum
number from an array of ten numbers.
5. Write a program to search a particular element from an array using
binary search. If the element is found set AX to one and otherwise to
zero.
6. Write a program to calculate the factorial of a number where factorial
is defined as:
factorial(x) = x*(x-1)*(x-2)*...*1
factorial(0) = 1
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