1. Springfield Technical Community College Center for Business and Technology

2. Decimal vs. Binary Decimal counting system is based on numbers 0 – 9 This is the numbering system we use everyday. This system is called a base 10 counting system. Since 0 – 9 totals 10 numbers The Binary number system is based on 2 numbers 0 and 1 Computers use this system because they can only understand on (1) and off (0) states. This system is called the Base 2 system as only 2 numbers are used

3. Binary Numbers Within a computer system binary code is used to represent letters and symbols. The ASCII Coding Scheme is a good example of this code. The computer uses an 8 bit code to represent the characters. Base 2 system = 2^8 This gives you 256 possible chars, 0 – 255 The ASCII code for a capital “J” is 74 Since computers only understand ones and zeros the 74 must be converted into Binary. How do we do this? It’s not hard!

4. Conversion Time Lets do a Decimal to Binary conversion using this chart. We need to place a 1 over each place holder that will equal 74. The rest will be zeros. 128 64 32 16 8 4 2 1 0 1 0 0 1 0 1 0 So 64 + 8 + 2 = 74, our Binary code is 01001010 And if we wanted to do a Binary to Decimal conversion all we need to do is place the known Binary code over the chart and add the ones.

5. Hexadecimal, Hexa What? Hexadecimal is a base 16 numbering system used in the new IPv6 addressing scheme and is easier to understand than Binary. Base 16 means it’s an alpha numeric system; 0 1 2 3 4 5 6 7 8 9 A B C D E F Base 16 = 0 – 9, then letters A – F = 10 – 15 16 total numbers

6. Hexadecimal Conversion Let’s work with the same numbers Convert a Decimal 74 into Hex. The Binary 8 bit chart is now divided into two 4 bit charts called Nibbles. 8 4 2 1 0 1 0 0 1 0 1 0 Now add the ones on each side. 4 10 4 A Now use the code – 0123456789ABCDEF 74 = 01001010 = 0x4A The 0x just denotes the code is Hex.

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