BitWithBiteCCNA Networking · Quick Reference
Module 5 — Number Systems Cheat Sheet
In one line: Computers use binary (base-2) because transistors — the fundamental building blocks of all processors and memory — have exactly two states: on (1) or off (0). Everything a compu...
Key Ideas
1Why Binary?. Computers use binary (base-2) because transistors — the fundamental building blocks of all processors and memory — have exactly two states: on (1) or off (0). Everythi...
2Binary Positional Notation. Just like decimal uses powers of 10 for position values (1s, 10s, 100s, 1000s), binary uses powers of 2. Each position in an 8-bit binary number has a fixed value. The...
3Binary to Decimal — 5 Worked Examples. To convert binary to decimal: write down the positional values (128, 64, 32, 16, 8, 4, 2, 1), multiply each by the corresponding bit (1 or 0), then add all results.
4Decimal to Binary — 5 Worked Examples. To convert decimal to binary using the subtraction method: start with the largest positional value (128). If the decimal number is >= 128, write 1 and subtract; oth...
5IP Addresses in Binary. An IPv4 address is really a 32-bit binary number written as four decimal octets for human readability. The subnet mask is also 32 bits: consecutive 1s identify the net...
Code Examples
Position: 128 64 32 16 8 4 2 1
Example 1: 11000000 = 192
Bits: 1 1 0 0 0 0 0 0
Values: 128 + 64 + 0 + 0 + 0 + 0 + 0 + 0 = 192
Example 2: 10101000 = 168
Bits: 1 0 1 0 1 0 0 0
Values: ...
Pos: 128 64 32 16 8 4 2 1
Convert 192 → binary
192 >= 128? YES → bit=1, remainder=64
64 >= 64? YES → bit=1, remainder=0
0 >= 32? NO → bit=0 (repeat for 16,8,4,2,1)
Result: 11000000
Convert 168 → binary
168-128=40, 4...
IP Address: 192.168.10.1 in binary:
192 = 11000000
168 = 10101000
10 = 00001010
1 = 00000001
Full: 11000000.10101000.00001010.00000001
Subnet mask: 255.255.255.0 in binary:
255 = 11111111 <-- network bits (all 1s)
255 = 11111111...