Bitwise Operations in Programming

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Processing Bits in the Integer Numbers
Bitwise Operations in Programming
Svetlin Nakov, PhD
Co-Founder, Innovation and
Inspiration Manager at SoftUni
https://nakov.com

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 The 4 groups of software development skills
 Coding, algorithms, development concepts, technologies
 Numerals systems
 Decimal, binary, hexadecimal
 Conversion between numeral systems
 Bitwise operations (&, I, ^, ~)
 Processing bits in programming
 Reading / writing bits from integers
 How to become a software developer?
Agenda

 Coding skills – 20%
 Algorithmic thinking – 30%
 Fundamental concepts of the
software developer profession – 25%
 Programming languages &
software technologies – 25%
Skills of Software Developers
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 Bit == the smallest unit of data used in computing
 Takes only one of two values: either a 0 or 1
 1 bit can store anything with two separate states
 Logical values (true / false)
 Algebraic signs (+ / -)
 Activation states (on / off)
 Bits are organized in computer memory in
sequences of 8 bits, called bytes (octets)
Bit
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 Bit – single 0 or 1, representing a bit of data
 Byte (octet) == 8 bits == the smallest addressable unit
in the computer memory
 KB (kilobyte) == 1024 bytes (sometimes 1000 bytes)
 MB (megabyte) == 1024 KB == 1048576 bytes
 GB (gigabyte) == 1024 MB == 1073741824 bytes
 TB (terabyte) == 1024 GB == 1099511627776 bytes
 PB (petabyte) == 1024 TB == 1125899906842624 bytes
Bit, Byte, KB, MB, GB, TB, PB
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5
101b
0x8
Numerals Systems
Decimal, Binary and Hexadecimal

 Numeral system == system for representing
numbers in written form using sequence of digits
 Positional numeral systems == the value of each
digit depends on its position
 These numeral systems has a base (e.g. 2, 10, 16)
Numeral Systems
Decimal
(base = 10)
Binary
(base = 2)
Hexadecimal
(base = 16)
30 111110 1E
45 101101 2D
60 111100 3C
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Decimal Numbers
 Decimal numbers (base 10)
 Represented using 10 numerals (called digits):
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
 Each position represents a power of 10
401 = 4*102 + 0*101 + 1*100 =
= 4*100 + 0*10 + 1*1 =
= 400 + 0 + 1 = 401
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Binary Numbers
 The binary system is used in computer systems
 Binary numbers (base 2)
 Represented by sequence of 0 or 1
 Each position represents a power of 2
5 -> 101b
101b = 1*22 + 0*21 + 1*20 = 4 + 0 + 1 = 5
11
1010b = 1*23 + 0*22 + 1*21 + 0*20 =
8 + 0 + 2 + 0 = 10

Binary and Decimal Conversion
 Binary to decimal
 Multiply each digit to its
magnitude (power of 2)
 Decimal to binary
 Divide to the base (2) until
0 is reached and take the
reminders in reversed order
1011b = 1*23 + 0*22 + 1*21 + 1*20 =
= 1*8 + 0*4 + 1*2 + 1*1 =
= 8 + 0 + 2 + 1 =
= 11
11 / 2 = 5 (1) // last digit
5 / 2 = 2 (1) // previous digit
2 / 2 = 1 (0) // previous digit
1 / 2 = 0 (1) // fist digit
Result: 1011
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>>
Bitwise Operations
Bitwise Operators and Bit Shifts

Bitwise Operators
 Bitwise operators work with the binary representations of
the numbers, applying bit by bit calculations
 The operator ~ turns all 0 to 1 and all 1 to 0 (like ! for
boolean expressions but bit by bit)
 The operators |, & and ^ behave like ||, && and ^
for boolean expressions but bit by bit
Operator | | | & & & ^ ^ ^
Operand1 0 1 1 0 1 1 0 0 1
Operand2 0 0 1 0 0 1 0 1 1
Result 0 1 1 0 0 1 0 1 0
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 Bitwise NOT (~)
 Bitwise AND (&)
Bitwise Operators – Examples
5 // 0101
~5 // 1010
5 // 0101
3 // 0011
5 & 3 // 0001
 Bitwise OR (|)
 Bitwise XOR (^)
5 // 0101
3 // 0011
5 | 3 // 0111
5 // 0101
3 // 0011
5 ^ 3 // 0110
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 Bit shifts are bitwise operations, where
 Bits are moved (shifted) to the left or right
 The bits that fall outside the number are
lost and replaced by 0
Bit Shifts
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 Left shift (<< operator)  Right shift (>> operator)
0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1
0 0 1 1 1 1 1 1

 How to get the last bit from a number n?
 The bits are numbered from 0, from right to the left
 The position of the last (rightmost) bit is 0
 Last bit – formula:
Bitwise Operations: Get the Last Bit
n = 125 // 01111101
mask = 1 // & 00000001
n & mask // 00000001 = 1
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lastBit = n & 1
1 1 1 0 10 1 1
4 3 2 1 07 6 5
n =
lastBit = 1

 How to get the bit at position p from a number n?
 Bit at position – formula:
Bitwise Operations: Get Bit at Position
n = 125 // 01111101
p = 5 // 5th position
125 >> p // 00000011 = 3
3 & 1 // 00000001 = 1
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bit = (n >> p) & 1
1 1 1 0 10 1 1
4 3 2 1 07 6 5
n =
p = 5
bit value = 1

 How to set the bit at given position p to 0 or 1?
 Assign a bit b (0 or 1) at position p – formula:
Bitwise Operations: Set Bit at Position
n = 125 // 01111101
mask = ~(1 << p) // 11011111
result = n & mask // 01011101
n = 125 // 01111101
mask = 1 << p // 00100000
result = n | mask // 01111101
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 Clear a bit (0) at position p  Set a bit (1) at position p
n = n & ~(1 << p) | (b << p)

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 Networking protocols
 Many devices communicate using bit-level protocols
 E.g. the SYN flag in the TCP protocol header is the bit #1 from the
14th byte in the TCP packets
 Web browsers use bitwise operations to connect to a Web site
 Many binary file formats use bits to save space
 E.g. PNG images use 3 bits to specify the color format used
 Data compression replaces byte sequences with bit sequences
 E.g. the DEFLATE algorithm in ZIP files
Why We Need Bitwise Operations?

How to Become a
Software Engineer?

 First find out if programming is for you!
 Sign up for the SoftUni free coding course
for beginners: https://softuni.bg/apply
 Or follow a tutorial / book / video course on the Internet
 Does programming excite you?
 Do you really like it and enjoy it?
 Are you good at coding problems?
 Do you want to write code all the time?
How do I Become a Software Engineer?
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 Coding skills – 20%
 Algorithmic thinking – 30%
 Fundamental concepts of the
software developer profession – 25%
 Programming languages &
software technologies – 25%
Learn the 4 of Fundamental Skills
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 To become a software engineer, you need to study
hard and consistently for 3000+ hours!
 2 years @ 4 hours daily (average)
 Or 1 year @ 8-10 hours daily
 Developing practical projects
 Write 100K+ lines of code (LOC)
 100K LOC == 300 days * 350 LOC
Study Hard, Very Hard!
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Learning Path: From Zero to First Job
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https://softuni.bg/apply
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Bitwise Operations in Programming

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