1. EECE.2160 ECE Application Programming
Instructors:
Dr. Lin Li & Dr. Michael Geiger
Fall 2019
Lectures 35 & 36:
Bitwise operators

2. ECE Application Programming: Lecture 35
Lecture outline
Announcements/reminders
M 12/9: Last day for P7 submissions (initial submission)
Th 12/12: last day of classes; P8 & Ch. 9 exercises due
P8 deals with structures (lectures 26-27, 29-30)
M 12/16: Exam 3, 3-6 PM, Ball 210
Will post course evals online; you’ll submit eval at exam
T 12/17: All code due by end of day
Program 9: Worth up to 4 points extra credit on final avg
Resubmission deadline for P6, P7, & P8
Today’s class
Bitwise operators
Common bitwise operations
3/14/2020
ECE Application Programming: Lecture 35

3. Binary and hexadecimal values
Humans operate in decimal (base 10)
Computers operate in binary (base 2)
Each digit is a bit (binary digit)
Hexadecimal (base 16) commonly used in programming
Leading “0x” in C programming indicates hex value
Base conversion
Binary  decimal: multiply bit 0 by 20, bit 1 by 21, etc.
e.g = (0 x 23) + (1 x 22) + (1 x 21) + (1 x 20) =
= = 710
Binary  hex: start with LSB and make 4-bit groups
e.g = 1B716
Note that an extra 0 is implied for the first group: 0010001
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ECE Application Programming: Lecture 35

4. Bitwise Logical Operations
Deal with individual bits of a value
Each bit is evaluated separately
There is no "Carry" as with addition…i.e. the results of an operation in one bit position has no effect on an adjacent bit.
Operators
&  AND
|  OR
^  XOR
~  bitwise NOT (flip all bits)
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ECE Application Programming: Lecture 35

5. Bitwise Logical Operations
AND A B
A&B 1
NOT A
~ A 1 OR
XOR (exclusive or) A B
A|B 1 A B
A^B 1
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ECE Application Programming: Lecture 35

6. Bitwise Logical Operations
& = ? A B
A&B 1
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7. Bitwise Logical Operations
& = ? A B
A&B 1
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ECE Application Programming: Lecture 35

8. Bitwise Logical Operations
& = ? A B
A&B 1
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ECE Application Programming: Lecture 35

9. Bitwise Logical Operations
| = ? A B
A | B 1
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ECE Application Programming: Lecture 35

10. Bitwise Logical Operations
ECE 160
02/02/2005
Bitwise Logical Operations
| = ? A B
A | B 1
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ECE Application Programming: Lecture 35
(c) 2005, P. H. Viall

11. Bitwise Logical Operations
| = ? A B
A | B 1
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ECE Application Programming: Lecture 35

12. Bitwise Logical Operations
^ = ? A B
A ^ B 1
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ECE Application Programming: Lecture 35

13. Bitwise Logical Operations
^ = ? A B
A ^ B 1
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ECE Application Programming: Lecture 35

14. Bitwise Logical Operations
^ = ? A B
A ^ B 1
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ECE Application Programming: Lecture 35

15. Bitwise Logical Operations
ABCD | FF00 &
FFCD
NOTE: & is a higher precedence than | similar to * being a higher precedence than + in algebra. A B
A&B
A|B
A^B 1
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ECE Application Programming: Lecture 35

16. ECE Application Programming: Lecture 36
Bit shifts
Bit shift operators
Left shift: <<
Right shift: >>
Shifts in 0s (with unsigned ints)
x << n shifts x left by n bits
Equivalent to x * 2n
e.g. 1 << 5 = ( ) << 5 =
x >> n shifts x right by n bits
Equivalent to x / 2n
e.g. 8 >> 3 = ( ) >> 3 =
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ECE Application Programming: Lecture 36

17. ECE Application Programming: Lecture 36
Review: C operators
Operator
Associativity
Innermost ( )
Left to right
Unary -, unary ~
Right to left
* / %
<< >>
NOTE: shift amt < 32
& ^ |
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ECE Application Programming: Lecture 36

18. Example: Bitwise operations
Evaluate each of the following expressions if you have the following unsigned ints:
A = 7, B = 10, and C = 0xFFFFFFFF
A & B
A | ~B
A ^ C
A << 4
B >> 5
A | (B << 2)
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ECE Application Programming: Lecture 36

19. ECE Application Programming: Lecture 36
Example: Solution
First step: convert A & B to binary (or hex)
A = 7 = = 0x7
B = 10 = = 0xA
Now solve problems
A & B = 0111 & 1010 = 00102
A | ~B = 0111 | ~1010
= 0111 | 0101 = Upper 28 bits = 1!
Final answer: 0xFFFFFFF7
A ^ C = ( ) ^ ( )
= = 0xFFFFFFF8
A << 4 = 0111 << (4 bits) = = 0x70
B >> 5 = 1010 >> (5 bits) = 0
Only lowest 4 bits of B contain non-zero values!
A | (B << 2) = | (1010 << 2 bits)
= 0111 | =
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ECE Application Programming: Lecture 36

20. ECE Application Programming: Lecture 36
Hexadecimal output
To print a number in hex, use %x or %X
%x prints characters a-f in lowercase
%X prints characters A-F in uppercase
To show leading 0x, use the # flag
To show leading 0s, use precision with total # digits
Field width + 0 flag also works unless value = 0
Examples (assume var1 = 0x1A2B)
printf(“%x”, var1)  1a2b
printf(“%X”, var1)  1A2B
printf(“%#x”, var1)  0x1a2b
printf(“%.6x”, var1)  001a2b
printf(“%#.6x”, var1)  0x001a2b
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ECE Application Programming: Lecture 36

21. Example: Common bitwise operations
Given an unsigned int, n, and a number, b, how would you:
Clear all bits of n?
Clear the lower 16 bits of n (mask out lower bits)?
Flip all bits of n?
Flip bit b of n?
Set bit b of n (i.e., make sure bit b is 1)?
Clear bit b of n (i.e., make sure bit b is 0)?
Note: 0 ≤ b ≤ 31; least significant (rightmost) bit is bit 0
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ECE Application Programming: Lecture 32

22. ECE Application Programming: Lecture 32
Example solution
Given an unsigned int, n, and a number, b, how would you:
Clear all bits of n?
n = 0;
Clear the lower 16 bits of n (mask out lower bits)?
X & 0 = 0, regardless of whether X = 0 or X = 1
Should AND lower 16 bits with 0
n = n & 0xFFFF0000;
Flip all bits of n?
n = ~n;
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ECE Application Programming: Lecture 32

23. Example solution (cont.)
Given an unsigned int, n, and a number, b, how would you:
Flip bit b of n?
X ^ 1 = ~X, regardless of whether X = 0 or X = 1
Need 1 in bit position b  (1 << b)
n = n ^ (1 << b);
Set bit b of n (i.e., make sure bit b is 1)?
X | 1 = 1, regardless of whether X = 0 or X = 1
n = n | (1 << b);
Clear bit b of n (i.e., make sure bit b is 0)?
As shown before, X & 0 = 0
To get 0 in specific bit position, shift 1 to that position and then invert bit mask: ~(1 << b)
n = n & ~(1 << b);
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ECE Application Programming: Lecture 32

24. Common bitwise operations
General operation
Logical operation
Bit mask values in positions that change
Bit mask values in positions staying same
Example: modify bits 8-23 (middle 16 bits)
Set bit(s)
Bits changed to 1 OR 1
n = n | 0x00FFFF00
Clear bit(s)
Bits changed to 0
AND
n = n & 0xFF0000FF
Flip bit(s)
All 0  1;
All 1  0
XOR
n = n ^ 0x00FFFF00
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ECE Application Programming: Lecture 32

25. ECE Application Programming: Lecture 32
Extracting bits
Very common to extract bits from larger value
One example: instruction decoding
Instruction: basic operation executed by processor
Decoding: figure out what each bit group “means”
First bits typically operation; others choose data to be used
Examples: 0xABCD1234 =
Lowest 16 bits = 0x1234
Upper 16 bits = 0xABCD
Bits = 0xAB
Bits 1-6  look at lowest 8 bits (bits 0-7)
 bits 1-6 = = 0x1A
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ECE Application Programming: Lecture 32

26. Extracting bits (cont.)
Isolate bits you want
AND with bit mask to clear unwanted bits
Positions you want to keep = 1
Positions you want to clear = 0
Examples:
To get lowest 16 bits  mask = 0x0000FFFF
To get upper 16 bits  mask = 0xFFFF0000
To get bits  mask = 0xFF000000
To get bits 1-6  mask = = 0x E
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ECE Application Programming: Lecture 32

27. Extracting bits (cont.)
Shift bits to right
Shift amount = original position of lowest bit
Examples:
Lowest 16 bits  bits 0-15  no shift
Upper 16 bits  bits  shift right by 16
Bits  shift right by 24
Bits 1-6  shift right by 1
Order doesn’t really matter
Could shift first and then AND to mask out upper bits
Can combine steps in single operation
Upper 16 bits of x = (x & 0xFFFF0000) >> 16
Bits 1-6 of x = (x & 0x E) >> 1
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ECE Application Programming: Lecture 32

28. ECE Application Programming: Lecture 35
Next time
Exam 3 Preview (Wednesday, 12/11)
Reminders:
M 12/9: Last day for P7 submissions (initial submission)
Th 12/12: last day of classes; P8 & Ch. 9 exercises due
P8 deals with structures (lectures 26-27, 29-30)
M 12/16: Exam 3, 3-6 PM, Ball 210
Will post course evals online; you’ll submit eval at exam
T 12/17: All code due by end of day
Program 9: Worth up to 4 points extra credit on final avg
Resubmission deadline for P6, P7, & P8
3/14/2020
ECE Application Programming: Lecture 35