Homework
• Turn in HW2 tonight
• HW3 is on-line already
• Questions?
1
Base for Integer Constants
• Designating the base for an integer constant
• If constant begins with either:
0x
0X
It is Hex with a-f as Hex digits
It is Hex with A-F as Hex digits
• Otherwise, if constant begins with
0
It is Octal
• Otherwise, it is decimal
23
Decimal 23
2
Base for Character Constants
• Designating the base for a character constant
• If constant begins with either:
‘\x
‘\X
It is Hex with a-f as Hex digits
It is Hex with A-F as Hex digits
• Otherwise, if constant begins with
‘\0
It is Octal
• Otherwise, it is the ASCII code for a character
‘a’
ASCII code for lower case character a
3
Signed/Unsigned Constants
• Constants are Signed by default!
• Important when converted to 32 bits of significance
– When sign bit (MSB) is equal to 0:
0x55 as a 32 bit quantity
0000 … 01010101
‘\x55’ as a 32 bit quantity
0000 … 01010101
When sign bit (MSB) is equal to 1:
0xaa as a 32 bit quantity
0000 … 10101010
‘\xaa’ as a 32 bit quantity
1111 … 10101010
4
What we’d expect to see!
• C Source Code
int i = 0x55; /* int set = to int constant */
int j = '\x55'; /* int set = to char constant */
printf("i= %x, j= %x\n", i, j);
• Executes and prints as
i= 55, j= 55
5
What Happened?
• C Source code
int i = 0xaa; /* int set = to int constant */
int j = '\xaa'; /* int set = to char constant */
printf("i= %x, j= %x\n", i, j);
• Executes and prints:
i= aa, j= ffffffaa
6
Signed (Default) Behavior
• Careful mixing modes when initializing variables!
int i = 0xaa;
int j = ‘\xaa’;
char
int
char
int
(= 000000aa) probably as intended
(= ff ff ff aa) sign bit extension!
Sign Bit Extension
0
00000000 00000000 00000000 0
Sign Bit Extension
1
11111111 11111111 11111111 1
7
Signed (Default) Behavior
• Careful mixing modes when initializing variables!
c = 0x23456789;
int
char
(= ‘\x89’) truncates MSBs
00100011 01000101 01100111 10001001
+
10001001
-
NOTE: char value is negative even though int was positive
8
Unsigned Behavior
• C Source Code
unsigned int i = 0xaa;
unsigned int j = '\xaa';
printf("i= %x, j= %x\n", i, j);
• Executes and prints as:
i= aa, j= aa
9
One’s Complement
Two’s Complement
• One’s Complement Character Arithmetic
~ is the one’s complement operator
~ flips the value of each bit in the data
All zeroes become one, All ones become zero
~’\xaa’ == ‘\x55’
~10101010 == 01010101
10
One’s Complement
Two’s Complement
• Two’s Complement Character Arithmetic
- is the two’s complement operator
- flips the value of each bit in the data and adds 1
It creates the negative of the data value
- ‘\x55’ == ‘\xab’
- 01010101 == 10101011
11
Two Special Case Values
• char 0 (or zero of any length)
-00000000
= 11111111
+
1
= 00000000
• char -27 (or -2n-1 for any length = n)
-10000000
= 01111111
+
1
= 10000000
12
Bit Manipulation
• Bitwise Operators:
~
&
|
^
<<
>>
unary not
and
or
xor (exclusive or)
leftshift
rightshift
• Operate on pair of bits of the input data values!
13
Binary Logic Tables
AND
NOT
~
0
OR
&
0
1
|
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
XOR
1
0
ADD
^
0
1
+
0
1
0
0
1
0
0
1
1
0
1
1
1
0
Carry 1
14
Bit Manipulation
unsigned char n = ‘\xa6’;
n
10100110
~n
01011001 (1s complement: flip bits)
n | ‘\x65’ 10100110 turn on bit in result if
| 01100101 on in either operand
11100111
15
Bit Manipulations
n & ‘\x65’ 10100110
& 01100101
00100100
n ^ ‘\x65’ 10100110
^ 01100101
11000011
turn on bit in result if
on in both operands
turn on bit in result if
on in exactly 1 operand
16
Bit Manipulations (Left Shift)
char n = ‘\x18’;
00011000
n << 1
00110000 shift 1 to left (like * 2)
n << 2
01100000 shift 2 to left (like * 4)
(MSBs disappear off left end)
Left Shift
0
n can be either signed or unsigned – no difference
Significance can be lost if data shifted too far left
17
Bit Manipulations (Right Shift)
unsigned char n = ‘\x18’; 00011000
n >> 1
00001100 shift 1 to right (like / 2)
n >> 2
00000110 shift 2 to right (like / 4)
(LSBs disappear off right end)
Integer truncation of divide by 2n just like with /
Unsigned Right Shift
0
18
Bit Manipulations (Right Shift)
signed char n = ‘\xa5’;
10100101
n >>1
11010010 (bring in a 1 from the left)
n >>2
11101001 (bring in two 1’s from left)
The rule is to bring in a copy of the sign bit!
Signed Right Shift
• Bringing in extra copies of the sign bit from the
left end is another form of "sign extension" 19
Bit Manipulations (Right Shift)
• For a signed variable, negative value shifted
right by 2 is still a negative value
• ‘\xa5’
== 10100101
• ‘\xa5’ >> 2 == 11101001 == ‘\xe9’
• Same result as divide by 4 (22 = 4)
20
Bit Manipulations (Right Shift)
• When right shifting a signed value:
Different rounding results for positive vs negative
Result stays negative – does not become positive
1>>1 = 0
Rounds down
-(1>>1) = 0 Rounds down then applies minus
(-1)>>1 = -1 Applies minus then rounds down
-1>>1 = -1
Applies minus then rounds down
• Rounding behavior not exactly same as /2
21
Converting Decimal to Binary
• From 11710 get binary by halving the number
successively (rounding down) and writing down the
digit 1 when have an odd result, 0 when result is even
(consider number itself the first result):
117
58
29
14
7
3
1
0
1 LSB
0
1
0
1
1
1
0 MSB
• Read UP and add any leading 0’s: 01110101 = ‘\x75’
22
Unsigned Binary to Decimal
• Treat each bit position n that contains a one as
adding 2n to the value. Ignore zeros because
they can’t add anything to the value.
Bit 0
Bit 1
Bit 2
Bit 3
Bit 4
Bit 5
Bit 6
Bit 7
Total
LSB
MSB
1
0
1
1
0
1
0
1
1
0
4
8
0
32
0
128
173
(= 20)
(= 22)
(= 23)
(= 25)
(= 27)
23
Signed Binary to Decimal
• Treat each bit position n that contains a one as
adding 2n to the value except treat the MSB as
subtracting 2n. (Ignore zeros as before)
Bit 0
Bit 1
Bit 2
Bit 3
Bit 4
Bit 5
Bit 6
Bit 7
Total
LSB
MSB
1
0
1
1
0
1
0
1
1
0
4
8
0
32
0
-128
-83
(= 20)
(= 22)
(= 23)
(= 25)
(= -27)
24
Converting Hex to Decimal
• Treat each digit n as adding 16n to the value.
Ignore zeros because they can’t add anything
to the value.
Digit 0
Digit 1
Digit 2
Digit 3
Digit 4
Digit 5
Digit 6
Digit 7
Total
LSBs
MSBs
0
2
b
0
0
1
0
0
0
32 (= 2 * 161)
2816 (= 11 * 162)
0
0
1048576 (= 1 * 165)
0
0
1051424
25