number formats

# number formats - MAE 3113 3-1 Number System We know that...

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School of Mechanical and Aerospace Engineering MAE 3113 3-1 Number System We know that the position of each digit in a decimal number is important and has meaning depending on it ‘location’ in the number. For example, lets look at the number 435.21 10 . The 4 is the most significant digit and the 5 is the least significant digit. Lets take a closer look at this number. 2 1 0 1 2 10 1 10 2 10 5 10 3 10 4 21 . 435 - - × + × + × + × + × = Or in a more general form = n m b b a N

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School of Mechanical and Aerospace Engineering MAE 3113 3-2 Since digital devices have only two states, a simple binary or base 2 numbing system is used for counting. 11010 2 However when using digital numbers one must be very careful with identifying the most significant bit. For example: 11010 can also be written as 01011 and have the same meaning. How is this possible? Binary Number System
School of Mechanical and Aerospace Engineering MAE 3113 3-3 This is possible because a digital number can arrive in two ways. 11010 2 1. Most significant bit (MSB) arrives first 1. Least significant bit (LSB) arrives first 1 1 0 1 0 0 1 0 1 1 Binary Number System

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School of Mechanical and Aerospace Engineering MAE 3113 3-4 Once the location of the MSB is known one can convert from the binary system to the decimal system by applying { } 1 , 0 2 = = a where a N n m b 0 1 2 3 4 2 0 1 0 1 1 26 2 0 2 1 2 0 2 1 2 1 0 1 2 3 4 = × + × + × + × + × Binary Number System n
School of Mechanical and Aerospace Engineering MAE 3113 3-5 Binary Number System Examples 0 1 2 3 4 2 5 1 1 0 1 0 1 43 2 1 2 1 2 1 2 1 0 1

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## This note was uploaded on 09/14/2011 for the course MAE 3113 taught by Professor Staff during the Fall '11 term at Oklahoma State.

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number formats - MAE 3113 3-1 Number System We know that...

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