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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