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Computer Science Class 9 L 2.2 Data Representation. How whole numbers and Integers are stored?
Data Representation in Computing System
Whole Numbers
Use of Whole Numbers
Integers
Negative Values
Minimum Integer value
The whole numbers consist of non-negative integers such as 0, 1, 2, 3 etc. The set of whole number is represented by W.
W = {0, 1,2,3,4, …………………}
Whole numbers are used to represent quantities that cannot be negative e.g.
Number of students in a class
Age of a person
Grade/Class of a student
A 1-byte integer has 8 bits to store values.
If all bits are on it represents the maximum value i.e. 111111112 which is 25510.
If all bits are off it represents minimum value 000000002 which is 010
Using 2 or 4 bytes we have more bits to store data
General formula for representing a maximum value is 2n – 1, where n is the number of bits
1-byte whole number (8 bits): maximum value = 28-1=255
2-byte whole number (16 bits): maximum value =216-1= 65,535
4-byte whole number (32 bits): maximum value = 232-1= 4,294,967,295
Integers
The integers are the whole numbers that can be positive, negative or zero. These numbers are not fractions or do not have decimal parts. The set of Integers is represented by Z
Z = {…….., -3, -2, -1, 0, 1,2,3,4, ………}
The integers include all positive and negative whole numbers i.e.
{……….., -3, -2, -1, 0, 1,2,3,…………………..}
The integers are represented by Z
Z = {0, ±1, ± 2, ± 3, ± 4, ……………}
In computer programming integers are called signed integers
To store both positive and negative values one bit is reserved as sign bit.
If the signed bit is ON(1), value is negative; otherwise, it is non-negative i.e. 0 or positive.
Using this system, the maximum positive values that can be stored in 1-byte signed integer is 011111112 that is equal to 12710
As the bits available to store a value are n-1, hence the maximum value will be 2n-1-1. We can use this formula to compute the maximum values of 2 and 4 bytes.
Negative Values
Negative values are stored using two’s compliment. To store negative values computer uses a method called two’s compliment. To find the two’s complement of a binary number, follow these steps:
1. Invert all bits (change 0s to 1s and 1s to 0s)
2. Add 1 to the Least Significant Bit (LSB)
Convert decimal number -5 to 8-bit binary number
1. Start with the binary representation of 5: 000001012
2. Invert all bits: 111110102
3. Add1: 111110102 + 12 = 111110112
So, -5 in 8-bit two’s complement is 111110112
Minimum Integer Value
For an 8-bit integer, we switch on the sign bit for the negative value and turn all bit ON.
Turn all bit
111111112
Except the first bit, we take two’s complement, we get
100000002 = 12810 = -128 = -27
Formula for calculating -2n-1, where n is the total number of bits.
2-Byte Integer (16 bits): Minimum value
= -2 16-1 =-215
= -32,768
4-Byte Integer (32 bits): Minimum value
= -232-1 = -231
= -2, 147, 483,648
It is important to understand how integers are stored in memory as it helps us to appreciate the inner working of computers and ensures us to effectively work with different data types in programming







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