Subject
Year
: Digital System
: 2009
Number System
Chapter 3
Overview
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Decimal Numbers
Binary Numbers
1's and 2's Complement
Signed Numbers
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Decimal Numbers
• In the decimal number system each of ten digits, 0 through 9, represents a certain
quantity.
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Binary Numbers
The binary number system is another way to represent quantities. It is less
complicated than the decimal system because it has only two digits. The decimal
system with its ten digits is a base-ten system; the binary system with its two
digits is a base-two system. The two binary digits are 1 and 0.
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Counting in Binary
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Counting in Binary con’t
Example Binary to decimal Conversion
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Counting in Binary con’t
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Decimal to Binary Conversion
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Decimal to Binary Conversion con’t
Repeated division-by-2 method
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1's and 2's Complement
• The 1’s complement of binary number is found by changing all 1s to 0s and all 0s
to 1s.
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1's and 2's Complement
• The 2’s complement of binary number is found by adding 1 to the LSB of the 1’s
complement
• 2’s complement = (1’s complement) + 1
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Signed Numbers
• A 0 sign bit indicates a positive number, and a 1 sign bit indicates a negative
number
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