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Lecture

Part 1 Lecture Notes Includes the first part of lecture notes for this course.


Department
Electrical and Computer Engineering
Course Code
ECE222
Professor
Anwar Hasan

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ECE222/Fall 2010/Hasan 1-1
Number Systems (Review)
Consider a binary n-tuple
B=bn1···b1b0, bi∈ {0,1}
Positional Number System, LSB, MSB
V(B) = bn12n1+···+b121+b020
What are max and min V(B)?
Example: B= 101 means V(B)=510
Different ways to represent signed numbers:
sign-&-magnitude, 1’s complement,
2’s complement (why in most computers?), etc.

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ECE222/Fall 2010/Hasan 1-2
Values in three different number systems:
BS&M 1’s 2’s
011 +3 +3 +3
010 +2 +2 +2
001 +1 +1 +1
000 +0 +0 +0
100 -0 -3 -4
101 -1 -2 -3
110 -2 -1 -2
111 -3 -0 -1

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ECE222/Fall 2010/Hasan 1-3
For +ve numbers in all the 3 systems
MSB=0
rest is magnitude
For -ve numbers in all the 3 systems
MSB=1
rest is
·magnitude (S&M)
·2n11magnitude(1’s)
·2n1magnitude (2’s)
+0 and -0 in S&M and 1’s complement
(a disadvantage. why?)
• −2n1in 2’s complement system only
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