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44 CHAPTER 2 / NUMBER SYSTEMS, BINARY ARITHMETIC, AND CODES

• Diminished radix complement representation
• Excess (offset) code representation

Of these, the radix 2 complement representation, called 2's complement, is the most widely
used system in computers.

2.6.1 Signed-Magnitude Representation
A signed-magnitude number in radix r consists of a magnitude \N\ together with a symbol
indicating its sign (positive or negative) as follows:

(2.11)

where the subscript rSM refers to signed-magnitude in radix r. Such a number lies in the
n l
1
decimal range of — (r"" — 1) through +(r ~ — 1) for n integer digits in radix r. The
fraction portion, if it exists, consists of m digits to the right of the radix point.
The most common examples of signed-magnitude numbers are those in the decimal and
binary systems. The sign symbols for. decimal (+ or — ) are well known. In binary it is
established practice to use the following convention:

0 denotes a positive number
1 denotes a negative number.

One of these (0 or 1) is placed at the MSB position of each SM number. Four examples in
8-bit binary are:

EXAMPLE 2.11

Magnitude

EXAMPLE 2.12

+0 10 = 0 0000000 2sM

EXAMPLE 2.13

Magnitude
-i23 =
10
t
Sign
Bit