Learning objectives
- Explain the purpose and scope of Number Systems and Binary Math.
- Identify important protocols, roles, fields, and terminology.
- Apply the concept to a practical network scenario.
- Use IOS XE commands to verify operational behavior.
1. Core concepts
Binary is base 2 and uses 0 and 1. IPv4 octet bit weights are 128, 64, 32, 16, 8, 4, 2, and 1. Add weights whose bits are set: 11000000₂ = 192; decimal 173 is 10101101₂.
2. How it works
Hexadecimal is base 16: 0–9 and A–F. One hex digit represents four bits (a nibble), and two hex digits represent one byte. Bitwise AND returns 1 only when both corresponding bits are 1; subnet masks use AND to isolate network bits.
Visual walkthrough
3. Worked example
Convert 172.16.5.10 to binary: 172 = 10101100, 16 = 00010000, 5 = 00000101, 10 = 00001010. AND 192.168.10.77 with 255.255.255.0 to get network 192.168.10.0.
IOS XE commands and verification
Syntax and feature availability can vary by device family and software release. Confirm platform support before applying configuration.
show ip interface brief show running-config | include ip address
Common mistakes and troubleshooting
- Check physical and interface state before changing higher-layer settings.
- Verify both ends agree on addressing, VLAN, encapsulation, and protocol parameters.
- Use operational show commands; configured text alone does not prove a feature is working.
- Change one variable at a time and verify the result.
Knowledge check
Choose one answer per question. Submit to see why the correct choice is right and why every other option is wrong. These are original practice questions, not Cisco exam questions.
Number Systems and Binary Math quiz
3 questions · explanations for every option · retry enabled