Base-2 (Binary) Number System

Master the language of computers - binary! Understanding base-2 is essential for cybersecurity professionals working with low-level systems, network protocols, and data representation.

What is Binary?

Binary (base-2) is the fundamental number system used by computers. It uses only two digits: 0 and 1, representing the two states of electronic switches: OFF and ON.

Why Binary? Electronic circuits can easily distinguish between two voltage levels (high/low), making binary the most reliable system for digital computing.
Key Characteristics:
  • Base: 2
  • Digits: 0 and 1 (called "bits")
  • Place Values: Powers of 2 (1, 2, 4, 8, 16, 32, etc.)
  • Usage: All digital computing, networking, data storage
Bit

Binary Digit (0 or 1)
Smallest unit of data

Byte

8 bits grouped together
Can represent 256 values (0-255)

Understanding Binary Place Values

Each position in a binary number represents a power of 2, starting from 2⁰ on the right.

Example: The binary number 11010110
2⁷
(128)		 2⁶
(64)		 2⁵
(32)		 2⁴
(16)		 2³
(8)		 2²
(4)		 2¹
(2)		 2⁰
(1)
1 1 0 1 0 1 1 0
128 64 0 16 0 4 2 0

Decimal Value: 128 + 64 + 16 + 4 + 2 = 214

Quick Tip: To convert binary to decimal, add up the place values where there's a 1.

Converting 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

Start from the left, double and add:

1011₂:
Start with 0
See 1: 0×2 + 1 = 1
See 0: 1×2 + 0 = 2
See 1: 2×2 + 1 = 5
See 1: 5×2 + 1 = 11₁₀

Converting Decimal to Binary

Method 1: Division by 2

Example: Convert 45₁₀ to binary

45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5  remainder 1
5  ÷ 2 = 2  remainder 1
2  ÷ 2 = 1  remainder 0
1  ÷ 2 = 0  remainder 1

Read remainders from bottom to top: 101101₂
Method 2: Powers of 2 Subtraction

Find the largest power of 2 that fits:

45₁₀:
45 - 32 (2⁵) = 13  → 1
13 - 16 (2⁴) = no  → 0
13 - 8  (2³) = 5   → 1
5  - 4  (2²) = 1   → 1
1  - 2  (2¹) = no  → 0
1  - 1  (2⁰) = 0   → 1

Result: 101101₂

Binary Arithmetic

Binary Addition
Rules:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (0 carry 1)

Example:
  1011
+ 1101
------
 11000
Binary Subtraction
Rules:
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow 1)

Example:
  1101
- 1010
------
  0011

Binary in Cybersecurity

1. IP Addresses and Subnet Masks

IPv4 addresses are 32-bit binary numbers:

192.168.1.1 = 11000000.10101000.00000001.00000001
255.255.255.0 = 11111111.11111111.11111111.00000000
2. File Permissions (Unix/Linux)

Permissions use 3 bits each for read, write, execute:

rwx = 111₂ = 7₁₀
r-x = 101₂ = 5₁₀
r-- = 100₂ = 4₁₀

chmod 755 = rwxr-xr-x
3. Bitwise Operations in Programming
Operation Symbol Example Use Case
AND & 1010 & 1100 = 1000 Masking bits
OR | 1010 | 1100 = 1110 Setting flags
XOR ^ 1010 ^ 1100 = 0110 Encryption
NOT ~ ~1010 = 0101 Bit flipping

Practice Exercises

Exercise 1: Binary to Decimal

Convert these binary numbers to decimal:

  1. 10110₂
  2. 11111111₂
  3. 10000001₂
Exercise 2: Decimal to Binary

Convert these decimal numbers to binary:

  1. 73₁₀
  2. 255₁₀
  3. 128₁₀
Exercise 3: Binary Operations

Perform these operations:

  1. 1011₂ + 1110₂
  2. 11001₂ - 1010₂
  3. 1100₂ AND 1010₂
Exercise 4: Real-World Application

Given the IP address 172.16.254.1, convert the first octet (172) to binary.

Interactive Binary Converter

Decimal to Binary
Binary to Decimal

Next Steps

Great job learning binary! Continue your journey:

Learn Hexadecimal
Understanding Bytes
Apply to Networking