Springfield Technical Community College Center for Business and Technology

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

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!

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 So = 74, our Binary code is 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.

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; A B C D E F Base 16 = 0 – 9, then letters A – F = 10 – total numbers

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 Now add the ones on each side A Now use the code – ABCDEF 74 = = 0x4A The 0x just denotes the code is Hex.

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