EE109 Signed Systems and Arithmetic
[Pages:54]11.1
Unit 11
Signed Representation Systems Binary Arithmetic
11.2
BINARY REPRESENTATION SYSTEMS REVIEW
11.3
Interpreting Binary Strings
? Given a string of 1's and 0's, you need to know the representation system being used, before you can understand the value of those 1's and 0's.
? Information (value) = Bits + Context (System)
Unsigned Binary system
01000001 = ?
BCD System
ASCII system
6510
41BCD
`A'ASCII
11.4
Binary Representation Systems
? Integer Systems
? Unsigned
? Unsigned (Normal) binary
? Signed
? Signed Magnitude ? 2's complement ? Excess-N* ? 1's complement*
? Floating Point*
? For very large and small (fractional) numbers
? Codes
? Text
? ASCII / Unicode
? Decimal Codes ? BCD (Binary Coded Decimal) / (8421 Code)
* = Not fully covered in this class
11.5
Signed Magnitude 2's Complement System
SIGNED SYSTEMS
11.6
Unsigned and Signed
? Normal (unsigned) binary can only represent positive numbers
? All place values are positive
? To represent BOTH positive and negative numbers we must use the available binary codes differently, some for the positive values and others for the negative values
? We call these signed representations
11.7
Signed Number Representation
? 2 Primary Systems
? Signed Magnitude ? Two's Complement (most widely used for integer
representation)
11.8
Signed numbers
? All systems used to represent
negative numbers split the
possible binary combinations in half (half for positive numbers /
1111 1110
0000 0001
0010
half for negative numbers)
? In both signed magnitude and 2's complement, positive and negative numbers are
1101
1100
-
1011
1010
0011
+
0100
0101 0110
separated using the MSB
1001
0111
1000
? MSB=1 means negative
? MSB=0 means positive
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