Lecture C5: Number representation
Please take a look at the handput "
Number Systems
" which has answers to lots of the muddy card
question's from this lecture.
Response to 'Muddiest Part of the Lecture Cards'
(53 respondents, out of 67students)
1)
Why is it important to know binary?
(and similar questions) (7 students)
Binary is crucial because 0’s and 1’s are the only language that a computer understands. All your high
level languages are transformed into machine language (fixed patterns of 0’s and 1’s). We will look at a
simple machine language in upcoming lectures.
2)
How to represent numbers w/ bit patterns?
(1 student)
The representation schemes such as ASCII, Hex, Binary coding, Floatpoint representations, all provide
means of representing numbers as bit patterns.
3)
How do we know what format of binary string is being used, how do we know which is best to
employ?
(and similar questions) (4 students)
Good question. There are number of ways (I am sure you can come up with your own scheme) of
representing a number in binary representation. There are standardization committees that decide which
formats are used and these are agreed upon universally.
4)
On slide number 2 in today's lecture, you show that 101101 = 37, but doesnt that equal 45?
(1
student)
It sure does! There is a typo in the figure I coiped from Brookshear (Figure 1.15). 101101 equals 45.
5 )
How do you store values w/ base 10 using ASCII?
(1 student)
In ASCII, we represent each symbol by an integer value. For example ‘a’ is using decimal number
system = 97 or using hexadecimal number system 61.
So the bit pattern to represent ‘a’ = 01100001
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6)
110 +100=010 = 2?
(1 student
)
1
1
0
+
1
0
0
1
0
1
0
If you have only three bits to represent the number, the ‘
1
’ is lost (this phenomenon is called overflow).
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 Winter '12
 CharlesColeman
 Aeronautics, Astronautics, Binary numeral system, Decimal, Rational number

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