Binary is the language of computers that uses 1s and 0s. It is used for IP addressing in networking. There are different methods to convert binary to decimal and decimal to binary, such as least significant digit and most significant digit. Calculators can check conversions.

1. INTRODUCTION TO BINARY
WHAT IT IS AND HOW IT IS USED FOR CISCO NETWORKING

2. OUTLINE
 What is binary?
 How is it used for CISCO networking?
 Translating Binary to Decimal
 Translating Decimal to Binary

3. WHAT IS BINARY?
 Binary is the language that computers and electronics use to communicate and send data
 Binary is a series of 1s and 0s – typically indicating a state of on (1) or a state of off (0)
 Positional notation refers to the fact that each 1 or 0 in a specific location refers to a specific
value – for example, the number 0010 = 2, because the 1 is in the position for the value of 2

4. HOW IS IT USED FOR CISCO NETWORKING
 CISCO networking, and any networking that utilizes the TCP/IP protocol suite, uses binary to
denote IP addresses. While most of the time one will see these addresses in decimal format (for
example 192.168.2.1), binary is actually used to create addresses and subnetworks.
 A typical IP address consists of 4 octets – each octet is 8 binary numbers long – for example,
the first octet, 192, in the address above would translate to 01100000 in binary. Notice that it is 8
characters long.

5. TRANSLATING BINARY TO DECIMAL
 Binary is based on a power of 2 system – i.e. each position in a binary number is the next power
of 2 – for example:
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
Position 8 Position 1

6. TRANSLATING BINARY TO DECIMAL
 To translate a binary number to a decimal number, use the positional table – for example,
translate the number 00110100 to binary:
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
0 0 1 1 0 1 0 0
First, place
the binary
number in
the chart
Next, add all of the numbers that have a 1
together
32 + 16 +4 = 62

7. NOW YOU TRY!
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
0 1 1 1 0 0 1 1
Convert 01110011 to decimal using the table:
Answer:
64+32+16+2+1 =115

8. TRANSLATING DECIMAL TO BINARY
 There are two methods for converting decimal to binary
 They are Least Significant Digit (LSD) and Most Significant Digit (MSD)
 MSD is the most common method and the method that CISCO tends to teach

9. TRANSLATING DECIMAL TO BINARY
Most Significant Digit Method (MSD)
 Starts at the highest Binary value (for networking,
this is 128)
 Step 1: Compare the value of the number to the
highest value, if the value is equal to or greater
than this value, a 1 is placed in the number and
the binary value is subtracted from the decimal
value (otherwise, skip to step 2)– for example:
156 is the value to translate
is 156 >= 128? YES!
So, a 1 is placed in the value for 128 and
128 is taken from 156
156- 128 = 28
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
1

10. TRANSLATING BINARY TO DECIMAL
 Step 2: Using your remainder of 28 from
Step 1, continue to compare it to the
other values until you find one it is
equal to or greater than – once you
have found that value, do the same
thing you did in step 1 and add a 1 to
the value and subtract it from the
decimal value
 Step 3: Continue this process until you
reach 0
 End: Once you reach 0 you are done –
if there are any remaining values, fill
them with 0s
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
1 0 0 1 1 1 0 0
28 >= 64? NO (place a 0)
28 >= 32? NO (place a 0)
28 >= 16? Yes!!! (Place a 1 and subtract)
28-16 = 12
12 >= 8? Yes!!! (Place a 1 and subtract)
12- 8 = 4
4 >= 4? Yes!!! (Place a 1 and subtract)
4-4 = 0
Stop!! You have reached 0! Fill any
remaining values with 0s
Binary: 10011100

11. NOW YOU TRY!
Answer:
122 >= 128? NO! (Place a 0)
122 >= 64? Yes!!! (Place a 1 and subtract)
122-64 = 58
58 >= 32? Yes!!! (Place a 1 and subtract)
58-32 = 26
26 >= 16? Yes!!! (Place a 1 and subtract)
26-16 = 10
10 >= 8? Yes!!! (Place a 1 and subtract)
10 – 8 = 2
2 >= 4? NO! (Place a 0)
2 >= 2? Yes!!! (Place a 1 and subtract)
2-2 = 0
STOP!!! You have reached 0 – fill in remaining values
with 0s
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
0 1 1 1 1 0 1 0
Convert 122 to binary using the MSD method:
Binary: 01111010

12. TRANSLATING BINARY TO DECIMAL
Least Significant Digit (LSD) Method
 Uses Division to calculate the number
 Starts at the smallest value (1) and progresses to the largest (128 for
networking purposes)
 N represents the decimal number, Q the result of the division, R the
remainder of the number, and B the binary value:
 Step 1: Divide N by 2, if there is a remainder, place a 1, if not, place a 0
 For example:
 In this example, the division by 2 leaves no remainder, so the binary value is 0
N Q R B
122 61 0 0

13. TRANSLATING BINARY TO DECIMAL
 Step 2: continue this process, substituting Q for N in each step – for
example:
N (Value) Q (Result of /2) Remainder Binary
Value
122 61 0 0
61 30 1 1
30 15 0 0
15 7 1 1
7 3 1 1
3 1 1 1
1 0 1 1
0 0 0 0
= 01111010
Step 3: Stop when you hit 0
Step 4: Starting at the
bottom, write out the binary
number

14. NOW YOU TRY!
 Convert 115 to Binary from Decimal using the LSD Method
N (Value) Q (Result of /2) Remainder Binary
Value
115 57 1 1
57 28 1 1
28 14 0 0
14 7 0 0
7 3 1 1
3 1 1 1
1 0 1 1
0 0 0 0
Answer:
= 01110011

15. CHECKING YOUR WORK
 There are binary calculators available for use that can
easily help you translate between binary and decimal as
well as act as a method of checking your work. The built in
calculator for Windows is one of these.
Windows Calculator:
 In the calculator, go to View  Programmer to switch to
programmer mode
 To convert decimal to binary, make sure that the type is
selected to Dec on the left, type in your number, then
change the type to Bin to translate to binary
 To convert binary to decimal, make sure that the type is
selected to Bin, then type in your number, then change the
type to Dec to translate to decimal
Type Selection

16. SUMMARY
 Binary is used in Networking for addressing
 Binary can be converted to decimal and decimal can be converted to binary using several
different methods
 Always check your work – you can use the built-in Windows Calculator to do so, or there are
several others available online