Transcript Some “facts” about software…

Data Representation – Chapter 3
Section 3-1
Terminology
• “Digital”
– Discrete, well defined values/steps
– Opposite of analog
– Analogy: digital is to analog as int is to
double
• “Binary”
– A system consisting of two states
– on/off, true/false, yes/no, high/low, 0/1
– Basis for modern computers
Terminology
• “Bit”
– Binary-digit
– Smallest unit of storage in modern
computers
Data Representation
• 1000001 – what does this “mean”?
– one million, one
– sixteen million, seven hundred seventy
seven thousand, two hundred, seventeen
– two hundred sixty two thousand, one
hundred forty five
– sixty five
– “A”
– AJMP assembly language instruction
Data Representation
• 1000001
– Decimal number
– Hexadecimal number
– Octal number
– Binary number
– ASCII character
– 8051 machine instruction
Number Systems
• A number system is defined by its base or
radix
– The number of unique digits used in the system
– Digits range in value from 0 to radix-1
– Larger values are created by stringing together
digits
• Resultant value is defined by
 di
all i
b
i
• d: digit, b: base, i: position with 0 being the first position
to the left of the “base point”, increasing to the left,
decreasing to the right
Number Systems
• Binary is convenient/efficient for use in a
computer…
– Electronic circuits can be easily designed to deal
with two distinct levels
• e.g. TTL 0-volts and 5-volts
• … but extremely inconvenient for human
consumption
– Humans were designed to work with ten distinct
levels
• e.g. fingers
• We’ll concentrate on decimal, hexadecimal,
octal, and binary
Conversion
• Base b to decimal, b = 2 (binary)
1001  1  2  0  2  0  2  1  2   9
• Decimal to base b
3
2
1
0
2
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–
Integer divide value by b
Output remainder
Repeat on quotient
Until quotient is zero
10
Value
Quotient
Value / 2
Remainder
Value % 2
9
4
1
4
2
0
2
1
0
1
0
1
Conversion
• Binary to octal
– Separate binary number into groups of 3
binary digits padding the left with 0’s if
necessary
– Convert groups to decimal digits
10012 -> 001 001 -> 118
Conversion
• Binary to hexadecimal
– Separate binary number into groups of 4
binary digits padding the left with 0’s if
necessary
– Convert groups to decimal digits
10102 -> 1010 -> 1016(?)
– Not exactly
• 1010—1510 -> A16—F16
• i.e. 0123456789ABCDEF
Conversion
• Octal to hexadecimal and hexadecimal
to octal
– Convert to binary then to the target radix
using previous methods
Conversion
• Octal and hexadecimal are useful when
working closely with the architecture
– Designing circuits
– Designing device interfaces
– Writing assembly language programs
• In such situations one is generally concerned
with bit patterns rather than the decimal value
• The conversions can be done in your head
Assignment
1. Write a Java program that takes in a decimal number and
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prints out the binary representation
prints out the octal representation
prints out the hexadecimal representation
2. Write a Java program that takes in an binary number and
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prints out the octal representation
prints out the decimal representation
prints out the hexadecimal representation
3. Write a Java program that takes in an octal number and
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prints out the binary representation
prints out the decimal representation
prints out the hexadecimal representation
4. Write a Java program that takes in a hexadecimal number and
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prints out the binary representation
prints out the octal representation
prints out the decimal representation
DO NOT utilize Java API functions
Integer.toHexString()
Integer.toOctalString()
Integer.toBinaryString()
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or any other API or formatting functions that I might have overlooked that do the conversions for you!!!
You are to do this by pulling digits from numbers using addition, subtraction, multiplication, division,
modulo, or any other arithmetic operators and then doing the specified mathematical operations for the
conversion
Assignment
• Turn in
– Print out of your code
– Print out of the results (inputs and outputs) of your
code (this can be screen shots)
– Please make sure your code actually works and
produces the proper answers (i.e. test your code!)
• Due Tuesday at the start of class
• Late assignments will received reduced credit