Overview

1
Overview

• Stack and the Heap
• malloc() and free()
• Pointers
• numbers in binary

2
C Memory Management

• C requires knowing where objects are in memory,
  otherwise don't work as expect
• Java hides location of objects
• C has 3 pools of memory
• Static storage global variable storage,
  basically permanent, entire program run
• The Stack local variable storage, parameters,
  return address(location of "activation records"
  in Java or "stack frame" in C)
• The Heap (dynamic storage) data lives until
  deallocated by programmer

3
Pointer Arithmetic

• Which of the following are valid? (and what do
  they mean?)
• pointer integer
• integer pointer
• pointer pointer
• pointer integer
• integer pointer
• pointer pointer
• compare pointer to pointer
• compare pointer to integer (to 0?)

4
The Stack

• Stack frame includes
• Return address
• Parameters
• Space for other local variables
• Stack frames contiguous blocks of memory stack
  pointer tells where top stack frame is
• When procedure ends, stack frame is tossed off
  the stack frees memory for future stack frames

SP
5
Who cares about stack management?

• Pointers in C allow access to deallocated memory,
  leading to hard to find bugs !
• int ptr () int y y 3 return
  ymain () int stackAddr,content
  stackAddr ptr() content
  stackAddr printf("d", content) / 3
  / content stackAddr printf("d", content)
  /13451514 /

6
The Heap (Dynamic memory)

• Large pool of memory, not allocated in
  contiguous order
• back-to-back requests for heap memory could
  result blocks very far apart
• where Java new command allocates memory
• In C, specify number of bytes of memory
  explicitly to allocate item
• int ptrptr (int ) malloc(4) / malloc
  returns type void , so need to cast to right
  type /
• malloc Allocates raw, uninitialized memory from
  heap

7
C Memory Allocation malloc()

• Instead of explicit number, for portability, use
  sizeof()
• int ptrptr (int ) malloc(sizeof(int))
• not a procedure will check type or a variable to
  turn into a number
• malloc() also for structure allocation
• struct DlistNode nodePtrnodePtr (struct
  DlistNode ) malloc(sizeof(struct DlistNode))
  
• Note unlike Java, C never frees memory
  programmer must explicitly free memory

8
C Memory Allocation free()

• free() is opposite of malloc()
• Deallocates the memory so that it may be re-used
  by malloc()
• Danger may accidentally deallocate memory when
  still have a pointer into it, causing the same
  problem as with pointers to stack space

9
C Memory Allocation

• Rule of thumb deallocate anything you're never
  going to use again
• If not too much, and program doesn't run a long
  time, then allocate a lot at the beginning and
  then let memory be freed when program ends
• Otherwise, end up with "Memory Leaks", that is,
  program gets bigger over time, and need to
  restart computer
• In a large program with shared data structures,
  how do you know when something can be deallocated?

10
Odds and Ends

• Structure declaration does not allocate memory
• Variable declaration does allocate memory
• If declare inside procedure, allocated on the
  stack
• If declare outside a procedure, allocated in
  static storage

11
Pointers to structures

• The C arrow operator (-gt) dereferences and
  extracts a structure field with a single
  operator.
• The following are equivalent

struct point p printf(x is d\n,
(p).x) printf(x is d\n, p-gtx)
12
p

• p difference
• increment by ??
• Char p, q
• While(p q)

13
Comparison

• How do you tell if X gt Y ?

14
Which base do we use?

• Decimal great for humans, especially when doing
  arithmetic
• Hex if human looking at long strings of binary
  numbers, its much easier to convert to hex and
  look 4 bits/symbol
• Terrible for arithmetic on paper
• Binary what computers use you will learn how
  computers do ,-,,/
• To a computer, numbers always binary
• Regardless of how number is written
• 3210 0x20 1000002
• Use subscripts ten, hex, two in book,
  slides when might be confusing

15
Limits of Computer Numbers

• Bits can represent anything!
• Characters?
• 26 letters ? 5 bits (25 32)
• upper/lower case punctuation ? 7 bits (in 8)
  (ASCII)
• standard code to cover all the worlds languages
  ? 16 bits (unicode)
• Logical values?
• 0 ? False, 1 ? True
• colors ? Ex
• locations / addresses? commands?
• but N bits ? only 2N things

Red (00)
Green (01)
Blue (11)
16
How to Represent Negative Numbers?

• So far, unsigned numbers
• Obvious solution define leftmost bit to be sign!
  
• 0 ? , 1 ? -
• Rest of bits can be numerical value of number
• Representation called sign and magnitude
• MIPS uses 32-bit integers. 1ten would be
• 0000 0000 0000 0000 0000 0000 0000 0001
• And - 1ten in sign and magnitude would be
• 1000 0000 0000 0000 0000 0000 0000 0001

17
Shortcomings of sign and magnitude?

• Arithmetic circuit complicated
• Special steps depending whether signs are the
  same or not
• Also, Two zeros
• 0x00000000 0ten
• 0x80000000 -0ten
• What would 2 0s mean for programming?
• Therefore sign and magnitude abandoned

18
Another try complement the bits

• Example 710 001112 -710 110002
• Called Ones Complement
• Note positive numbers have leading 0s, negative
  numbers have leadings 1s.

• What is -00000 ? Answer 11111
• How many positive numbers in N bits?
• How many negative ones?

19
Shortcomings of Ones complement?

• Arithmetic still a somewhat complicated.
• Still two zeros
• 0x00000000 0ten
• 0xFFFFFFFF -0ten
• Although used for awhile on some computer
  products, ones complement was eventually
  abandoned because another solution was better.

20
Standard Negative Number Representation

• What is result for unsigned numbers if tried to
  subtract large number from a small one?
• Would try to borrow from string of leading 0s,
  so result would have a string of leading 1s
• 3 - 4 ? 000011 - 000100 111111
• With no obvious better alternative, pick
  representation that made the hardware simple
• As with sign and magnitude, leading 0s ?
  positive, leading 1s ? negative
• 000000...xxx is gt0, 111111...xxx is lt 0
• except 11111 is -1, not -0 (as in sign mag.)
• This representation is Twos Complement

21
2s Complement Number line N 5
00000
00001

• 2 N-1 non-negatives
• 2 N-1 negatives
• one zero
• how many positives?

11111
11110
00010
0
-1
1
2
11101
-2
-3
11100
-4
. . .
. . .
15
-15
-16
01111
10001
10000
22
Twos Complement for N32

• 0000 ... 0000 0000 0000 0000two
  0ten0000 ... 0000 0000 0000 0001two
  1ten0000 ... 0000 0000 0000 0010two
  2ten. . .0111 ... 1111 1111 1111 1101two
  2,147,483,645ten0111 ... 1111 1111 1111
  1110two 2,147,483,646ten0111 ... 1111 1111
  1111 1111two 2,147,483,647ten1000 ... 0000
  0000 0000 0000two 2,147,483,648ten1000 ...
  0000 0000 0000 0001two 2,147,483,647ten100
  0 ... 0000 0000 0000 0010two
  2,147,483,646ten. . . 1111 ... 1111 1111
  1111 1101two 3ten1111 ... 1111 1111 1111
  1110two 2ten1111 ... 1111 1111 1111
  1111two 1ten
• One zero 1st bit called sign bit
• 1 extra negativeno positive 2,147,483,648ten

23
Twos Complement Formula

• Can represent positive and negative numbers in
  terms of the bit value times a power of 2
• d31 x -231 d30 x 230 ... d2 x 22 d1 x 21
  d0 x 20
• Example 1111 1100two
• 1x-29 1x28 1x27... 1x220x210x20
• -29 28 27 ... 22 0 0
• -128 64 32 16 8 4
• -128 12
• -4ten

24
Twos complement shortcut Negation

• Change every 0 to 1 and 1 to 0 (invert or
  complement), then add 1 to the result
• Proof Sum of number and its (ones) complement
  must be 111...111two
• However, 111...111two -1ten
• Let x ? ones complement representation of x
• Then x x -1 ? x x 1 0 ? x 1 -x
• Example -4 to 4 to -4x 1111 1111 1111 1111
  1111 1111 1111 1100twox 0000 0000 0000 0000
  0000 0000 0000 0011two1 0000 0000 0000 0000
  0000 0000 0000 0100two() 1111 1111 1111 1111
  1111 1111 1111 1011two1 1111 1111 1111 1111
  1111 1111 1111 1100two

25
Twos comp. shortcut Sign extension

• Convert 2s complement number rep. using n bits
  to more than n bits
• Simply replicate the most significant bit (sign
  bit) of smaller to fill new bits
• 2s comp. positive number has infinite 0s
• 2s comp. negative number has infinite 1s
• Binary representation hides leading bits sign
  extension restores some of them
• 16-bit -4ten to 32-bit
• 1111 1111 1111 1100two
• 1111 1111 1111 1111 1111 1111 1111 1100two

26
Signed vs. Unsigned Variables

• Java just declares integers int
• Uses twos complement
• C has declaration int also
• Declares variable as a signed integer
• Uses twos complement
• Also, C declaration unsigned int
• Declares a unsigned integer
• Treats 32-bit number as unsigned integer, so most
  significant bit is part of the number, not a sign
  bit

27
Numbers represented in memory

• Memory is a place to store bits
• A word is a fixed number of bits (eg, 32) at an
  address
• Addresses are naturally represented as unsigned
  numbers in C

00000
01110
101101100110
11111 2k - 1
28
Negative Numbers

• Sign Magnitude
• First bit is the sign, rest of the bits are the
  value
• Get two negatives and addition is hard (try it)
• 2s compliment
• Only one zero, arithmetic is easy
• Add a number to its inverse and get 0
• Just flip the bits and add one to negate
• Sign extend if needed
• Now we need to worry about overflow!
• Signed vs. unsigned int

29
Signed v. Unsigned Comparisons

• X 1111 1111 1111 1111 1111 1111 1111 1100two
• Y 0011 1011 1001 1010 1000 1010 0000 0000two
• Is X gt Y?

unsigned YES signed NO
30
What if too big?

• Binary bit patterns above are simply
  representatives of numbers. Strictly speaking
  they are called numerals.
• Numbers really have an infinite number of digits
• with almost all being same (000 or 111) except
  for a few of the rightmost digits
• Just dont normally show leading digits
• If result of add (or -,,/) cannot be represented
  by these rightmost HW bits, overflow is said to
  have occurred.

31
And in Conclusion...

• We represent things in computers as particular
  bit patterns N bits ? 2N
• numbers, characters, ...
• Decimal for human calculations, binary to
  understand computers, hexadecimal to understand
  binary
• 2s complement universal in computing cannot
  avoid, so learn
• Computer operations on the representation
  correspond to real operations on the real thing
• Overflow numbers infinite but computers finite,
  so errors occur