1.3.7 Binary and Hexadecimal

What are the three main numbering systems used in networking?

1. Decimal (Base 10): The system we use every day.

2. Binary (Base 2): The system computers actually use.

3. Hexadecimal (Base 16): The system humans use to make binary easier to read.

What is Binary (Base 2)?

A numbering system where each digit can only be one of two values: 0 or 1. This is the fundamental language of all computers.

• How it works: Each position represents a power of 2 (1, 2, 4, 8, 16, 32, etc.).

• Example: The binary number 1011 is $(1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) = 11$ in decimal.

What is a byte or octet?

A group of 8 binary digits (bits).

• Example: The binary value 11111111 is one octet. In decimal, this equals 255, which is the highest value an octet can represent.

• Networking Use: An IPv4 address (like 192.168.1.1) is made of four decimal numbers, each representing one octet.

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What is Hexadecimal (Base 16)?

A numbering system where each digit can be one of 16 values.

• Values: 0-9 and then A, B, C, D, E, F (representing 10-15).

• Why it's used: It's a convenient shorthand for binary, as it's much shorter and easier for people to read and write.

• Networking Use: MAC addresses (hardware addresses) are written in hex, like 00:1A:2B:3C:4D:5E.

What is the simple conversion trick between Hexadecimal and Binary?

One hex digit represents exactly four binary digits (which is called a "nibble").

• Example:

  • The hex digit F = the binary value 1111

  • The hex digit A = the binary value 1010

• This makes it easy to convert long binary strings. The 8-bit byte 11111111 becomes the two-digit hex value FF.