Base-2 (Binary) Number System
The fundamental language of computers - understanding binary as the foundation of all digital systems and cybersecurity applications.
Learning Objectives
- Understand binary as the fundamental computer number system
- Learn binary place values and conversion methods
- Explore binary arithmetic and bitwise operations
- Apply binary concepts to cybersecurity scenarios
Binary Fundamentals
What is Binary?
Binary uses only two digits: 0 and 1
These represent electronic switch states:
0
OFF
1
ON
Binary Units
1
Bit
Smallest unit
8
Byte
8 bits = 256 values
Binary Place Values
Each position represents a power of 2:
1
2⁷ = 128
1
2⁶ = 64
0
2⁵ = 32
1
2⁴ = 16
0
2³ = 8
1
2² = 4
1
2¹ = 2
0
2⁰ = 1
11010110₂ = 128 + 64 + 16 + 4 + 2 = 214₁₀
Conversion Methods
Binary to Decimal
Method 1: Place Value Addition
Example: Convert 1011₂ to decimal
1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰)
= (1×8) + (0×4) + (1×2) + (1×1)
= 8 + 0 + 2 + 1 = 11₁₀
Method 2: Doubling Method
Example: Convert 1011₂ to decimal
Start with leftmost bit: 1
Double and add next: (1×2) + 0 = 2
Double and add next: (2×2) + 1 = 5
Double and add next: (5×2) + 1 = 11
Decimal to Binary
Division by 2 Method
Example: Convert 13₁₀ to binary
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Read remainders upward: 1101₂
Binary Arithmetic
Addition Rules
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (carry 1)
Bitwise Operations
AND Operation (&)
1010 & 1100 = 1000
Only 1 when both bits are 1
OR Operation (|)
1010 | 1100 = 1110
1 when either bit is 1
Cybersecurity Applications
IP Address Representation
IPv4 addresses are 32-bit binary numbers divided into 4 octets:
192.168.1.1
↓
11000000.10101000.00000001.00000001
File Permissions
Unix file permissions use 3-bit binary groups:
Network Subnetting
Subnet masks use binary to define network boundaries:
255.255.255.0 = 11111111.11111111.11111111.00000000
24-bit network, 8-bit host portion