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Lecture_02

# Lecture_02 - Lecture 2 Digital Systems and Binary Numbers...

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Lecture 2: Digital Systems and Binary Numbers Matthew Shuman October 2nd, 2009 1 Complements — 1-5 in Text The meaning of complement is something required to make a thing complete. For example, salsa complements tortilla chips, beer complements pizza, an ice cream cone complements a hot sum- mer day, and apple sauce complements pork chops. A key concept to explore is how two things complement each other. For example, when a piece of pizza is removed from a whole pizza the piece complements what is left behind and vice versa. Each of the 4 following complements use the same concept except in different bases and what is considered a complete number in that base. 1.1 Diminished Radix Complement The diminished radix complements are called by the radix - 1 . The diminished complement for a decimal number is the 9’s complement and 1’s complement for a binary number. 1.1.1 9’s Complement The 9’s complement finds whatever is needed to make an entire set of 9’s. This is shown in the example below. Finding the 5 digit 9’s complement of 1357 All 9 s 99999 Initial V alue - 01357 - - -- 9 s Complement 98642 The 5 digit 9’s complement of 1357 is 98642 1.1.2 1’s Complement The 1’s complement finds whatever is needed to make an entire set of 1’s. This is shown in the example below. Finding the 8 digit 1’s complement of 01101100 All 1 s 11111111 Initial V alue - 01101100 - - - - - - - 9 s Complement 10010011 The 8 digit 1’s complement of 01101100 is 10010011 1.2 Radix Complement

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