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Unformatted text preview: Chapter 2: Binary Values and
Chapter
Number Systems
• Information may be reduced to its fundamental state by means of binary
Information
numbers (e.g., on/off, true/false, yes/no, high/low, positive/negative).
numbers
• “Bits” (binary digits) are used to accomplish this. Normally, we
Bits”
consider a binary value of 1 to represent a “high” state, while a binary
value of 0 represents a “low” state.
value
• In machines, these values are represented electronically by high and
In
low voltages, and magnetically by positive and negative polarities.
low Chapter 2
Binary Values
Binary
and Number
Systems
Systems
Page 1
Page Binary Numerical Expressions
Binary
• Binary expressions with multiple digits may be viewed in the same way
Binary
that multidigit decimal numbers are viewed, except in base 2 instead of
base 10.
base
• For example, just as the decimal number 275 is viewed as 5 ones, 7
For
tens, and 2 hundreds combined, the binary number 01010110 can be
viewed in righttoleft fashion as...
viewed 01010110
01010110
01010110
01010110
01010110
01010110
01010110
0101011
1010110 •
•
•
•
•
•
•
• 0 ones
1 two
1 four
0 eights
1 sixteen
0 thirtytwos
1 sixtyfour
0 one hundred twentyeights So, 01010110
So,
is equivalent to
the decimal
number 2 + 4 +
16 + 64 = 86
16
Chapter 2
Binary Values
Binary
and Number
Systems
Systems
Page 2
Page Hexadecimal (Base16) Notation
Hexadecimal
• As a shorthand way of writing lengthy binary codes, computer
As
scientists often use hexadecimal notation.
hexadecimal
Binary Hexadecimal
Binary Hexadecimal
Code
Notation
Code
Notation
0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 For example, the binary
For
expression
1011001011101000 may
be written in
hexadecimal notation
as B2E8.
as
The two expressions
The
mean the same thing,
mean
but they are in different
notations.
notations Binary Hexadecimal
Binary Hexadecimal
Code
Notation
Code
Notation
1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F Chapter 2
Binary Values
Binary
and Number
Systems
Systems
Page 3
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 Fall '08
 Klein,S
 Computer Science

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