Guideline:

This is a Binary Conversion Help group. Post questions, suggestions, clarifications, examples, or any other inquiry or helpful information related to converting numbers from binary to decimal and/or decimal to binary.

Here are two Example of student’s work

Student A:

Converting from Binary to Decimal and Decimal to Binary is quite confusing for some people as they don’t quite understand exactly how to do this. There is a relatively easy way of doing this if you actually break it down. I am going to use IP (Internet Protocol) Addressing when doing this explanation specifically IPv4. For instance say you have an IP Address of 192.16.0.174 and you wish to convert this from decimal format to binary format. First you need to know that each IPv4 Address is contained with 4 octets being 192, 16, 0, and 174. Each octet is represented by 8 binary digits and if they are all being represented (turned on) then you will have a total of 256. The easiest way to represent this is by writing down on a piece of paper each binary digit at the top of the page. You know there are 256 total per octet so if you start off writing from left to right you will first write down 128 (half of 256), then you will half that until you reach one. See the example below.

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1

Once you have written this out it is much easier to transform decimal numbers into binary form. I have divided the numbers just so there is a better visualization taking place. So back to our previous example if you take the IP Address from above 192.16.0.174 we can easily convert this into binary form. As you probably know already a computer can only read 1’s and 0’s. With any device you will notice that the power switch has a 1 for on and an 0 for off. Same thing will apply hear a 1 means that it is turned on and an 0 means that it is turned off. Lets look at this even further as I have broken down our IP Address into binary form:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 Binary form Decimal Form

l l 0 0 0 0 0 0 = 11000000 = (128+64) = 192

0 0 0 l 0 0 0 0 = 00010000 = 16

0 0 0 0 0 0 0 0 = 00000000 = 0

l 0 l 0 l l l 0 = 10101110 =(128+32+8+4+2) = 174

Notice how easy that is all you have to do is copy it over which will give you your binary form. Now you also see that there is a decimal form following the binary form. If you were given a binary form and had to convert it back into a decimal form I have done this as well. All you simply have to do it just add up the total bits that you have “turned on” (represented by a 1) and that will give you your decimal form. I hope that I have not confused you more. It is way easier to explain when sitting with the other person and using a white board. Hope this was helpful!

Student B:

Base Conversion Converting a number to other kinds of number systems Binary Decimal Combinations of 0 to 9 Dec=10 Base 10 Combinations of 0 & 1 Bin=2 Base 2 e.g 1011 e.g. 100 2 read as 1011 base 2 read as
100 base 10 10 1011 2 = 2 0 2 1 2 2 2 3 1 0 1 1 2 100 10 10 0 1 2 = 10 10 1 0 0 10 Laws of Exponent Review your powers of 2 128 . 2 5 2 2 = 2 5 2 + = 2 7 = Bin->Dec 2 0 2 1 2 3 1 0 1 1 2 8 2 1 + + = 11 10 get the power of 2 equivalent of all 1s in the given number. Dec->Bin 11 10 1. Find a power of 2 number that is close to the given number but wont exceed the given number. Subtract these until you get 0. 8 11 – = 3 2 – = 1 1 – = 0 2 0 2 1 2 3 2. Convert to its exponential form the power of 2 numbers that you subtracted in the previous equation. 8 11 – = 3 2 – = 1 1 – = 0 4 bits binary length is 4 3. Plot the number of digits basing on the given 2 0 2 1 2 2 2 3 given length is 4 equation. Put 0 on the empty place values to complete the number. 1 2 1 1 0 length. Put 1 on the place value of the power of the 2 number that was used in the equation.