The document discusses stack data structures and their implementation in CPU organization. It describes stacks as last-in, first-out (LIFO) data structures that support two main operations: push and pop. It then covers register and memory-based stack implementations, including the use of stack pointers, data registers, and algorithms for push and pop in each case. The key difference is that register stacks grow with increasing addresses while memory stacks grow with decreasing addresses. The document concludes with an example of how stacks are used to evaluate arithmetic expressions by operating on the top two elements of the stack.

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2. STACK
 Stack is a data structure in which last item inserted is taken
out first
 It works in LIFO manner (last in first out)
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3. OPERATIONS ON STACK
 We can perform two operation on a stack
 INSERTION (PUSH)
 DELETION (POP)
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4. STACK ORGANIZATION
IN STACK ORGANIZATION WE STORE OR PLACE OUR
DATA IN A MANNER OF A STACK.
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5. STACK POINTER
 It’s an register which is used to store the address of the top
item in the stack
 It’s a 6-bit register
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6. DATA REGISTER
Whatever value we INSERT(PUSH) or DELETE(POP)
from the stack it stores in data register
It’s a 2byte register /16bits
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7. TYPES OF STACK ORGANIZATION
There are two types of stack organization we have for our
CPU
 REGISTER STACK
 MEMORY STACK
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8. REGISTER STACK
 If we have for example finite number of words which we
want to insert at top of another and making stack out of it
through register stack.
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9. SINGLE BIT REGISTER
We have two single bit registers
 FULL: If the entire stack is full then this full register will
set to be 1
 EMPTY: If the entire stack is empty then this empty
register will set to be 1
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10. ALGORITHM FOR PUSH
 SPSP+1
 M{SP}DR
 IF(SP=0)THEN (F1)
 EMPTY0
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11. ALGORITHM FOR PUSH
STEP BY STEP
 SPSP+1 Increment stack by a value 1
 M{SP}DR Whatever content present in data register
place it inside the memory word to which stack pointer is
presently pointing
 IF(SP=0)THEN (F1) We are performing push
operation so we may encounter a position where our stack
would become full so we have to set our full bit to 1
 If our stack pointer is equal to zero set full=1
 EMPTY0 Because we are putting values into the stack
so its not empty anymore
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12. ALGORITHM FOR POP
 DRM{SP}
 SPSP-1
 IF {SP=0}{EMPTY1}
 FULL0
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13. ALGORITHM FOR POP
STEP BY STEP
 DRM{SP}Whatever content I have in the memory word
that the stack pointer is pointing at present store it in the
data register
 SPSP-1 The stack pointer should point to the next top
element ,it must be decremented by a value-1
 IF{SP=0}{EMPTY1} We are performing POP operation
so we may encounter a position where our stack would
become entirely empty at that point we will set empty =1
 FULL0 Because we are deleting values from stack so its
obvious that it wont become full at any point
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14. MEMORY STACK
 In Memory stack we have a Memory Unit
 In memory unit we divide memory into 3 portions
 PROGRAM(INSTRUSTIONS): it is use to access/fetch
instructions from memory
 DATA(OPERANDS): it is use to access/fetch data and
operands from memory
 STACK: it is use to push or pop item into the stack
 In memory stack our stack grows with decreasing address
 There is different algorithm for both memory and register
stacks
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15. MEMORY UNIT
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16. ALGORITHM’S
PUSH POP
SPSP-1
M{SP}DR
DRM{SP}
SPSP+1
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17. ALGORITHM FOR PUSH
STEP BY STEP
 SPSP-1 The first operation we will do is we will
decrement our stack pointer
 M{SP}DR Whatever data we have in the data register we
should place it at the memory word at which the stack
pointer is pointing at
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18. ALGORITHM FOR POP
STEP BY STEP
 DRM{SP} Whatever content I have in the memory word
of stack pointer I have to place it into data register
 SPSP+1 Then we’ll increment our stack pointer by 1
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19. DIFFERENCE BETWEEN
REGISTER STACK AND MEMORY STACK
 The stack grows with
increasing address in
register stack
 Register stack is generally
on the CPU
 Access to register stack is
fast
 Register stack is limited size
wise
 The stack grows with
decreasing address in
register stack
 Memory stack is on the
RAM(main memory)
 Access to memory stack is
not as fast as register stack
 Memory stack is larger then
register stack size wise
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20. PRACTICAL APPLICATION
OF HOW STACK
ORGANIZATION WORKS
INSIDE OUR CENTRAL
PROCESSING UNIT
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21. DIFFERENT NOTATIONS WE HAVE IN
REPRESENTING ARITHMETIC NOTATIONS
 INFIX
 PREFIX (POLISH NOTATION)
 POSTFIX (REVERSE POLISH NOTATION/RPN)
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22. INFIX NOTATION
 In INFIX notation we have to write the operator in
between the operands
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23. PREFIX NOTATION
 In PREFIX notation we have to write the operator before
the operands
 Most of the computer use PREFIX notation to execute
arithmetic operations
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24. POSTFIX
(REVERSE POLISH NOTATION/RPN)
 In POSTFIX notation we have to write the operator after
the operands
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25. EXAMPLE:
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26. SO WHAT THE COMPUTER DOES?
 It scan the particular expression from left to right whenever
it encounters an operator it does the particular operation on
the previous two elements/operands that are scanning
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27. HOW STACK ORGANIZATION
IS USE TO EVALUATE
ARITHEMATIC
EXPRESSIONS
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28. WHEN AN OPERATOR IS
ENCOUNTERED
 The two top most elements in the stack are use for the
operation
 The stack is popped and the result of the operation replaces
the lower operand
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29. EXAMPLE:
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