The Understanding of Binary Math & Conversion By: David Paehlke

Base 10 Numbers Compared to Base 2 Numbers Base 10 numbers are 0 through 9 which are Decimal Numbers Base 2 numbers are 0 and 1 which are Binary Numbers 0 means off 1 means on

Names for Groups of Binary Digits One binary digit equals a bit Four binary digits equals a nibble Eight binary digits equals a byte

Converting Binary to Decimal For Our Understanding We use the number line: 128 64 32 16 8 4 2 1 Check Out This Site: A tutorial on binary numbers

Question #1: What are the digits for Binary? 0 through 9 0 and 1 0 through 9 and A through F

So Sorry! Time for Review

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The structure of Binary Digits Typically we work with 8 bits, a byte when dealing with binary numbers with computers and networking. The biggest number we can have is when all 8 bits are 1’s. Like this: 11111111 = 255 Which is: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1= 255

Let’s Practice Converting Decimal to Binary Take the decimal number 128 and convert it to Binary using our number line. Place a 0 for off and a 1 for on to equal 128. 64 32 16 8 4 2 1 1 0 0 0 0 0 0 0 So 10000000 in binary = 128 in decimal

Let’s try another one Let’s take the decimal number 149. 128 64 32 16 8 4 2 1 1 0 0 1 0 1 0 1 Just add the numbers together that have a 1 128 + 16 + 4 + 1 = 149

Here is one more Convert decimal number 231 to binary 128 64 32 16 8 4 2 1 1 1 1 0 0 1 1 1 128 + 64 + 32 + 4 + 2 + 1 = 231

Quiz Time! What is the decimal number 179 in binary? A. 10110011

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YOU ARE ABSOLUTELY CORRECT!

Now That You Can Convert From Decimal To Binary, Let’s Try Converting From Binary To Decimal As long as you can remember the number line you learned earlier, you should have no issues with this conversion. 128 64 32 16 8 4 2 1

Let’s Try One Let’s take the binary number 10101010 and convert it to decimal 128 64 32 16 8 4 2 1 1 0 1 0 1 0 1 0 We have: 128 + 32 + 8 + 2 = 170

Here is Another One The Binary number is 11110001 Our number line is: 64 32 16 8 4 2 1 1 1 1 1 0 0 0 1 128 + 64 + 32 + 16 + 1 = 241

Here is a website for more information on converting Binary to Decimal http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH065.HTM

Let’s try another example Let’s take 01101110 and convert it to decimal 64 32 16 8 4 2 1 0 1 1 0 1 1 1 0 We have 64 + 32 + 8 + 4 + 2 = 110

I Believe it is Time for a Quiz Question Convert 11000111 to Binary A. 201 B. 176 C. 199 D. 198

I am so Sorry, but that is incorrect

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CONGRATULATIONS!! You Have Completed the First Step in Learning Binary Math and Conversion with Binary and Decimal