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ECE 15A
Fundamentals of Logic Design
Lecture 2
Malgorzata Marek-Sadowska
Electrical and Computer Engineering Department
UCSB
Representing negative numbers
A negative number is usually indicated by its complement.
2’s complement
is the most common.
Example:
2
+11
:
00001011
-11
:
10001011
(signed magnitude)
11110100
(signed one’s complement)
11110101
(signed two’s complement)
Signed 2’s complement has only one representation for 0 (+)
One's complement format - 8 bit arithmetic
Change the number N to binary, ignoring the sign.
Add 0s to the left of the binary number to make a
total of 8 bits
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If the sign is positive, do nothing.
If the sign is negative, complement every bit (i.e.
change from 0 to 1 or from 1 to 0)
In this way we compute (2
-1) - N
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One's Complement
to Decimal
Convert the following 1's complement
representation to decimal:
a)
11110001
Since the sign bit is 1, complement the number:
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00001110
Convert to decimal:
00001110
2
= 14
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Put a negative sign in front:
-14
b)
00011010
->
26
Example
Write 25 in one's complement
0 0 0 1 1 0 0 1
25
W it
25 i
'
l
t
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Write -25 in one's complement
Since the number is negative, complement each bit
1 1 1 0 0 1 1 0
-25
Two's complement format - 8 bit arithmetic
Most computers today use 2's complement
representation for negative numbers.
The 2's complement of a negative number N is
obtained by adding 1 to the 1's complement.
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This is the same as computing 2 - N
For -13
00001101
base integer
11110010
1's complement
+1
11110011
2's complement
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