Lecture 2: Digital Systems and Binary Numbers
Matthew Shuman
October 2nd, 2009
1
Complements — 15 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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 Fall '08
 Wallace
 Binary numeral system, AND gate, radix complement

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