Representation of Signed Numbers - R.D.Sivakumar

1. R.D.SIVAKUMAR, M.Sc., M.Phil., M.Tech.,
Assistant Professor of Computer Science &
Assistant Professor and Head, Department of M.Com.(CA),
Ayya Nadar Janaki Ammal College,
Sivakasi – 626 124.
Mobile: 099440-42243
e-mail : sivamsccsit@gmail.com
website: www.rdsivakumar.blogspot.in
REPRESENTATION OF SIGNED NUMBERS

2.  If computers represent non-negative integers(unsigned) only.
 Computers represent negative integers(signed) only.
 The leftmost bit is 0, the number is positive.
 The leftmost bit is 1, the number is negative.
REPRESENTATION OF SIGNED NUMBERS
Sign+magnitude representation
0100 = +4
1100 = -4
The left most bit indicate the sign “0” indicates the positive.
And “1” indicates the negative.

3.  Change every 0 to 1 and every 1 to 0 .
 Add 1 to the result.
 Taken to pad(fill with zero) the original value out to the full representation width
before applying this algorithm.
 8-bit representation to store the number.
2’s COMPLEMENT REPRESENTAION
.
The binary equivalent of 23 is 10111.
Pad with zeros to make 8-bit pattern 00010111.
Invert all the bits 11101000.
Add 1 to the result 11101001.

4. Manual method to represent signed integers
in 2’s complement form
 This is an easier approach to represent signed integers.
 This is for –ve numbers only.
Step 1: Copy the bits from right to left, through and including the first 1.
Step 2: Copy the inverse of the remaining bits.
Example 1:
To represent –4 in a 4-bit representation:
The binary equivalent of the integer 4 is 0100
As per step1, copy the bits from right to left, through and including the
first 1 => 100
As per step2, copy the inverse of the remaining bits => 1 100 => -4
Example 2:
To represent –23 in a 8-bit representation:
The binary equivalent of 23 is 00010111
As per step 1: 1
As per step 2: 11101001 => -23

5. Interpretation of unsigned and signed integers
X = 1001
Y = 0011
Comparing two binary number for finding which is greater, the comparison
Depends on whether the numbers are considered as signed or unsigned numbers.
(X>Y) is this true or false
If X is greater than Y because they are unsigned.
If X is less than Y because they are signed.

6. Range of unsigned and signed integers
.
In a 4-bit system, the range of unsigned integers is from 0 to 15, that is, 0000 to
1111 in binary form. Each bit can have one of two values 0 or 1. Therefore, the total
number of patterns of 4 bits will be 2 X 2 X 2 X 2 = 16. In an n-bit system, the total
number of patterns will be 2n.. Hence, if n bits are used to represent an unsigned
integer value, the range is from 0 to 2n-1, that is, there are 2n different values.
In case of a signed integer, the most significant (left most) bit is used to represent
a sign. Hence, half of the 2n patterns are used for positive values and the other half
for negative values. The range of positive values is from 0 to 2n-1-1 and the range
of negative values is from –1 to –2n-1. In a 4-bit system, the range of signed
integers is from –8 to +7.