April 2011 ~ Toni Sugianto

This method is a conventional form used by humans to express a number in binary form. Here the representation of positive and negative numbers are distinguished only by the sign alone. Usually positive or negative sign indicated by the leading digits of the binary form, to representation by a certain number of digits. Example:

+5 ® + ® 101 or 5 101 (in binary)

-5 ® - 101
Note: sign (+) are usually ignored

If x is non-negative integers then x 'negative binary number of x such that x + x' = R

                               R = 2 (pangkat) N

                               N = maximum number of digits

                               x '= R - x

Answers Duties:
When N = 3, then R = 2 (pangkat) 3 = 8

        x = 5 ® 101

        x '= R - x

           = 8-5 = 3 ® 11 (in binary) .............(- 3)

If x is non-negative integers then x 'negative binary number of x such that x + x' = R

                               R = 2 (pangkat) N - 1

                               N = maximum number of digits

                               x '= R - x

Answers Duties:
When N = 3, then R = 2 (pangkat) 3-1 = 7

        x = 5 ® 101

        x '= R - x

           = 7-5 = 2 ® 10 .............. (-2)
Notes
For R = 2 (rank) N and R = 2 (pangkat) N - 1, integers that can be kept in storage for the 2nd way is:
2 (pangkat) (N-1) - 1
For R = 2 (pangkat) 3, the largest integer = 2 (pangkat) 2 -1, then r = 3 represents a number from -3 to +3

1. SCHEME TWO's complement

X = -3 ............... X '= 8-3 = 5 .......... X' = 101 (in binary)
X = -2 ................ X '= 8-2 = 6 .......... X' = 110
X = -1 ................. X '= 8-1 = 7 ......... X' = 111

2. ONE SCHEME's complement

X = -3 ............... X '= 7-3 = 4 .......... X' = 100 (in binary)
X = -2 ................ X '= 7-2 = 5 .......... X' = 101
X = -1 ................. X '= 7-1 = 6 ......... X' = 110

INTEGER	SIGN & MAGNITUDE	TWO’S COMPLEMENT	ONE’S COMPLEMENT
-3	-11	101	100
-2	-10	110	101
-1	-01	111	110
0	00	000	000
1	01	001	001
2	10	010	010
3	11	011	011