Decimal and Binary Explained

Real networkers don’t just connect cables — they connect logic.

When 10 Becomes 2: Base 10 is for humans. Base 2 is for engineers.

First Listen: let your ears lead the way before your mind takes notes.

Then read: let your eyes explore before your mind starts to explain.

Decimal and Binary in Plain English

Computers don’t understand words or decimal numbers the way humans do — they only understand binary, which is a numbering system made up of just two symbols: 1 and 0. Each of these digits represents an electrical state inside the computer’s hardware:

• 1 means ON (an electrical signal is present).
• 0 means OFF (no electrical signal).

Every piece of data — whether it’s text, numbers, images, or sound — is ultimately converted into these binary signals so that the computer’s processor and memory can store, process, and transmit information. While humans use the decimal system (base 10) because it’s intuitive for counting with our ten fingers, computers use binary (base 2) because it perfectly aligns with their electronic nature — circuits that can be either on or off.

Humans use the decimal system (base 10), which is built around ten digits — 0 and 9. Each digit’s position represents a power of 10, depending on its place value: 123 = (1 × 10²) + (2 × 10¹) + (3 × 10⁰)

When we write the number 123, each digit has a value based on its position:

Digit	Position (Power of 10)	Calculation	Value
1	Hundreds (10² = 100)	1 × 100	100
2	Tens (10¹ = 10)	2 × 10	20
3	Ones (10⁰ = 1)	3 × 1	3

Total: 100 + 20 + 3 = 123

That’s how the decimal system works — each position is 10 times bigger than the one to its right.

Computers, on the other hand, use the binary system (base 2), which relies only on two digits — 1 and 0. Each position represents a power of 2: 1011 = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 11 in decimal

Binary is the language of computers. Every instruction, piece of data, and signal in a computer system is ultimately expressed using combinations of 1s and 0s — representing ON and OFF electrical states.

In networking, understanding binary is crucial because key elements like IP addresses, subnet masks, and MAC addresses are all handled internally in binary form. While we write them in decimal (like 192.168.10.1) or hexadecimal (like 00:1A:2B:3C:4D:5E) for convenience, computers still process them as binary values — that’s how all network devices actually make their decisions.

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How It Appears in Cisco CLI

You won’t directly type binary numbers into a Cisco router, but understanding them helps interpret subnet masks and IP ranges.

Behind the scenes:

• 192 = 11000000
• 168 = 10101000
• 1 = 00000001
• 1 = 00000001

So, IPv4 address 192.168.1.1 is equal to 11000000.10101000.00000001.00000001 in binary.

Quick Reference Table

Base	Name	Digits Used	Example	Each Position Represents	Common Use
2	Binary	0, 1	1011	Powers of 2 (1,2,4,8,16…)	IP, MAC, Subnets
10	Decimal	0–9	123	Powers of 10 (1,10,100…)	Human counting, IP notation

Binary – The SIMPLEST explanation of Counting and Converting Binary numbers

Acknowledgment: This excellent video — “Binary – The SIMPLEST explanation of Counting and Converting Binary Numbers” — was created by Ed Harmoush, founder of PracticalNetworking.net. Shared here with full credit to the author for his outstanding contribution to networking education. Ed has a remarkable talent for simplifying complex topics into clear, accessible explanations.

Binary-to-Decimal Conversion

Category: Number Systems
Difficulty Level: CCNA Foundation

Step-by-Step Conversion Process

Let’s convert binary → decimal using this method:

Convert 11010 to decimal.

1. Write down the powers of 2 under each digit (starting from right):
   • Binary: 1 1 0 1 0
   • Powers: 16 8 4 2 1
2. Multiply each binary digit by its power of 2:
   • (1×16)= 16
   • (1×8)= 8
   • (0×4)= 4
   • (1×2)= 2
   • (0×1)= 0
3. Add the results: 16 + 8 + 0 + 2 + 0 = 26
4. Result: binary 11010 = decimal 26

Critical Evaluation of the Concept

Aspect	Strength	Weakness
Simplicity	Only two symbols (0 and 1); ideal for electronic circuits.	Harder for humans to read large binary strings.
Reliability	0/1 states resist electrical interference better than analog signals.	Not intuitive for arithmetic; needs conversion for human readability.
Precision	Perfect for logic-based computation, routing tables, and IP addressing.	Tedious for manual work (why we use decimal/hexadecimal shorthand).

So while binary is efficient for machines, decimal and hexadecimal are more convenient for humans — networking engineers often move between all three.

CCNA Exam Tips

Remember this pattern:

You’ll use it constantly in subnetting and IP calculations.

Shortcut technique for CCNA:

Memorize powers of 2 up to 128.
Practice converting binary octets to decimal quickly — e.g.
11100000 = 224
11111100 = 252
11111110 = 254

Summary

Binary-to-Decimal Conversion is the foundation of all network addressing and routing logic. It transforms simple on/off signals into meaningful numbers — enabling computers to calculate IP ranges, subnet boundaries, and broadcast addresses. Understanding binary isn’t just math — it’s learning to “see” the digital world the way routers and switches do. Once you master it, subnetting, IP planning, and routing tables all start making logical sense.

Binary-to-decimal conversion teaches how computers think. Each bit is a power of two, and converting between binary and decimal is the bridge between human-readable IP addresses and the raw binary logic inside every network device. For the CCNA exam, memorize powers of 2, visualize bit positions, and practice converting subnet masks until it becomes second nature.

Decimal-to-Binary Conversion

Decimal-to-Binary Conversion is the process of transforming a human-readable number (base 10) into a machine-readable format (base 2).
In simple terms, we’re translating from our human counting language—which uses ten digits— 0 and 9. into the language of computers, which use only two digits— 0 and 1.

Humans are comfortable with the decimal system because we have ten fingers. That’s why everything around us—prices, distances, time—uses base 10. Computers, on the other hand, have no fingers; they have electrical circuits that can only be ON (1) or OFF (0). These two states form the foundation of the binary system, base 2.

The Mathematical Process

Let’s break it down step by step. To convert a decimal number into binary, we repeatedly divide the number by 2 and record the remainders. Each remainder represents one binary bit— 0 and 1, starting from the least significant bit (rightmost).

Convert 77 (decimal) to binary.

Division	Quotient	Remainder
77 ÷ 2	38	1
38 ÷ 2	19	0
19 ÷ 2	9	1
9 ÷ 2	4	1
4 ÷ 2	2	0
2 ÷ 2	1	0
1 ÷ 2	0	1

Now read the remainders from bottom to top: 1001101

To make it a full byte (8 bits), we add a leading zero: 01001101

Result: 64+8+4+1 = 77

So, 77 (decimal) is equal to 01001101 (binary).

Visualizing Binary vs. Decimal

Let’s look at how numbers compare between systems:

Notice how 255 is the maximum number representable by 8 bits—all switches ON (1s).

Binary in Cisco CLI Context

When configuring routers or switches, you might not manually type binary numbers, but every decimal number you enter is interpreted in binary by the device. Let’s explore an example.

Assigning an IP Address

Router(config)# interface gigabitEthernet0/0
Router(config-if)# ip address 192.168.10.5 255.255.255.0
Router(config-if)# no shutdown

Behind the scenes, the router translates:

192.168.10.5 = 11000000.10101000.00001010.00000101
255.255.255.0 = 11111111.11111111.11111111.00000000

That binary mask means the first 24 bits identify the network, and the last 8 bits identify hosts.

Applying Binary Thinking in Troubleshooting

Binary knowledge helps you:
Calculate subnet ranges without a calculator.
Understand why an IP belongs (or doesn’t belong) to a network.
Identify wildcard masks in ACLs.
Verify interface configurations in CLI output.

Quick Practice

Let’s practice converting a few numbers:

1. Decimal 10 to Binary ?
   • Divide by 2:
     • 10 ÷ 2 = 5 (0)
     • 5 ÷ 2 = 2 (1)
     • 2 ÷ 2 = 1 (0)
     • 1 ÷ 2 = 0 (1)
       Binary = 1010
       
2. Decimal 25 to Binary ?
   • Divide by 2
     • 25 ÷ 2 = 12 (1)
     • 12 ÷ 2 = 6 (0)
     • 6 ÷ 2 = 3 (0)
     • 3 ÷ 2 = 1 (1)
     • 1 ÷ 2 = 0 (1)
       Binary = 11001
       
3. Decimal 192 to Binary ?
   • 128 fits at bit 7 = 1
   • Remaining 64 fits at bit 6 = 1
   • Remaining 0 fits at rest bits = 0
     Binary = 11000000

Cisco CLI Example – Subnet View

Let’s visualize how a router interprets an IP and mask:

Router# show ip interface gigabitEthernet0/0
GigabitEthernet0/0 is up, line protocol is up
  Internet address is 192.168.10.5/24
  Broadcast address is 192.168.10.255
  Address determined by configuration file

Internally:

• Network = 192.168.10.0 = 11000000.10101000.00001010.00000000
• Broadcast = 192.168.10.255 = 11000000.10101000.00001010.11111111

Every /24 (mask 255.255.255.0) means the first 24 bits belong to the network, and 8 bits remain for hosts.

Summary: Key Cisco CLI Commands for Troubleshooting Binary/Network Logic

Purpose	Command	Description
View interface IPs and masks	show ip interface brief	Shows assigned IPs in decimal but device stores them in binary
View detailed subnet information	show ip interface	Displays prefix length and broadcast address
Check routing table	show ip route	Understands networks by their binary prefixes
Test connectivity	ping	Confirms if host bits and network bits align correctly
Verify ACLs	show access-lists	Evaluates binary matches using wildcard masks
Convert subnet mask to prefix	show running-config	include ip address`

Binary conversion might feel mechanical at first, but it’s the foundation of everything in networking. Think of it as learning to “speak the native language” of routers and switches. Once you understand how 1s and 0s represent every packet, every IP, and every mask, you move from being a user of networking to being a builder of networks—someone who not only configures but understands what’s happening beneath the surface. When you can read binary fluently, subnetting becomes second nature, and troubleshooting feels like reading your own handwriting.

Hands-On Exercise: Decimal ↔ Binary Conversion

Objective

Learn how to think like a computer by converting numbers from the decimal system (base 10) —used by humans— into the binary system (base 2) —the language of computers and networking devices. You will do these conversions manually (without a calculator) and then verify your answers using the online tool provided at the end.

Convert Decimal to Binary

Convert the following 10 decimal numbers to their 8-bit binary equivalents (1 byte). Show all your steps (division by 2 and remainders) or use the subtraction-of-powers-of-2 method.

5 — 10 — 18 — 25 — 32 — 77 — 128 — 155 — 200 — 255

Tip: Remember the bit weights: 128, 64, 32, 16, 8, 4, 2, 1
Example: 77 → 01001101 → (64 + 8 + 4 + 1 = 77)

Convert Binary to Decimal

Now convert the following 10 binary numbers into decimal. Show the value of each “1” bit (the powers of 2 you’re adding).

00001010 — 00011100 — 00101101 — 01000011 — 01100110 — 01111111 — 10000000 — 10101010 — 11001100 — 11111111

Verify Your Answers Online: After completing both exercises, visit the following link to verify your answers and confirm your results. Visit Decimal – Binary converter and enter your numbers in the converter and verify whether your manual results match.

Summary

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