C++ Read in Binary Number as Negative
Negative Binary Numbers
Negative numbers can exist distinguishable with the help of actress bit or flag called sign bit or sign flag in Binary number representation system for signed numbers. It is not possible to add minus or plus symbol in front of a binary number because a binary number can take only two symbol either 0 or 1 for each position or chip. That's why we utilise this extra scrap called sign bit or sign flag. The value of sign flake is ane for negative binary numbers and 0 for positive numbers.
When an integer binary number is positive, the sign is represented by 0 and the magnitude by a positive binary number. When the number is negative, the sign is represented by 1 just the remainder of the number may be represented in one of iii possible means: Sign-Magnitude method, 1'due south Complement method, and two'south complement method. These are explained as following beneath.
one. Signed Magnitude Method:
In this method, number is divided into two parts: Sign scrap and Magnitude. If the number is positive and so sign bit will exist 0 and if number is negative then sign fleck will be 1. Magnitude is represented with the binary form of the number to be represented.
Example:Allow we are using v $.25 register. The representation of -5 to +five will be as follows:
Range of Numbers:For k bits register, MSB will exist sign bit and (k-1) $.25 will be magnitude. Positive largest number that can be stored is (2(k-1)-1) and negative lowest number that tin be stored is -(2(k-1)-one).
Note that drawback of this organization is that 0 has two different representation one is -0 (e.thousand., i 0000 in 5 chip register) and second is +0 (e.g., 0 0000 in five scrap register).
ii. 1's Complement Method:
Positive numbers are represented in the same fashion equally they are represented in sign magnitude method. If the number is negative then it is represented using 1's complement. First stand for the number with positive sign and then have 1'due south complement of that number.
Example:Let we are using 5 bits annals. The representation of -five and +5 volition be as follows:
+5 is represented as it is represented in sign magnitude method. -five is represented using the post-obit steps:
(i) +five = 0 0101
(2) Take 1'south complement of 0 0101 and that is 1 1010. MSB is 1 which indicates that number is negative.
MSB is always i in case of negative numbers.
Range of Numbers:For k bits register, positive largest number that can be stored is (two(yard-ane)-1) and negative lowest number that tin be stored is -(ii(k-1)-i).
Note that drawback of this arrangement is that 0 has two unlike representation ane is -0 (e.one thousand., 1 1111 in five bit register) and 2d is +0 (e.thousand., 0 0000 in five bit register).
3. 2's Complement Method:Positive numbers are represented in the same way as they are represented in sign magnitude method. If the number is negative then it is represented using ii's complement. First correspond the number with positive sign and so take 2'southward complement of that number.
Instance:Let nosotros are using 5 bits registers. The representation of -5 and +5 will be as follows:
+5 is represented as it is represented in sign magnitude method. -5 is represented using the following steps:
(i) +5 = 0 0101
(two) Take two'southward complement of 0 0101 and that is 1 1011. MSB is 1 which indicates that number is negative.
MSB is always one in case of negative numbers.
Range of Numbers:For k $.25 annals, positive largest number that can be stored is (2(g-1)-1) and negative everyman number that tin can be stored is -(2(m-1)).
The advantageof this system is that 0 has only one representation for -0 and +0. Aught (0) is considered as ever positive (sign bit is 0) in 2's complement representation. Therefore, it is unique or unambiguous representation.
These are representation method for signed binary numbers.
Published on 21-Feb-2019 10:16:02
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Source: https://www.tutorialspoint.com/negative-binary-numbers
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