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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=bnâˆ’1Â·Â·Â·b1b0, biâˆˆ {0,1}
Positional Number System, LSB, MSB
V(B) = bnâˆ’12nâˆ’1+Â·Â·Â·+b121+b020
What are max and min V(B)?
Example: B= 101 means V(B)=510
Diï¬€erent ways to represent signed numbers:
sign-&-magnitude, 1â€™s complement,
2â€™s complement (why in most computers?), etc.

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ECE222/Fall 2010/Hasan 1-2
Values in three diï¬€erent number systems:
BS&M 1â€™s 2â€™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
â€¢For +ve numbers in all the 3 systems
â—¦MSB=0
â—¦rest is magnitude
â€¢For -ve numbers in all the 3 systems
â—¦MSB=1
â—¦rest is
Â·magnitude (S&M)
Â·2nâˆ’1âˆ’1âˆ’magnitude(1â€™s)
Â·2nâˆ’1âˆ’magnitude (2â€™s)
â€¢+0 and -0 in S&M and 1â€™s complement