What is the process of converting information such as text numbers photos or music into digital data that can be manipulated by digital devices?

Data Representation refers to the form in which data is stored, processed, and transmitted. Devices such as smartphones, iPods, and computers store data in digital formats that can be handled by electronic circuitry. Digitization is the process of converting information, such as text, numbers, photo, or music, into digital data that can be manipulated by electronic devices. 

Data representation in computers

Computers are classified according to functionality, physical size and purpose. Functionality, computers could be analog, digital or hybrid. Digital computers process data that is in discrete from whereas analog computers process data that is continuous in nature. Hybrid computers on the other hand can process data that is both discrete and continuous.

In digital computers, the user input is first converted and transmitted   as electrical pulses that can be represented by tow unique states ON and OFF. The ON state may be represented by a “1” and the OFF state by a “0”. The sequence of ON’s and OFF’s forms the electrical signals that the computer can understand.

Number systems used in computing

When typing letters or words using the computer, these words or letters are represented by the computer as numbers it can understand. While this group of numbers that the computer can understand is called a ‘Number System’ the limited number of numerals in the number system called digits. The value of these numbers (numerals) depends on the position they occupy within the number. While the concept of number system was present in the ‘Abacus ‘ considered as the first calculating machine of the world, it has progressed up to the computer of today.

Binary number system

Though we use the decimal number system when we input numbers as data or instructions, the computer represents these data as 0 and 1. The number system which consists of 0 and 1 is the binary number system. The digits for the binary number system is given below.

Octal number system

 The number system which uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7 is called the octal number system. Digits of the octal number system are given below.

Hexadecimal number system

The computer uses binary numbers and it is difficult for human beings to read them. Hence, the hexadecimal number system is used as it is easier for humans to use. Normally, calculations are performed using the ten fingers of the hands. Just imagine you have sixteen fingers on your hands. Then you can use sixteen numbers to count. In the hexadecimal number system, ten digits are used from 0 to 9 and for the other 6 digits, A, B, C, D, E and F symbols are used. Here, A, B, C, D, E and F are used to represent 10, 11, 12, 13, 14 and 15.

The Digits of the hexadecimal number system are given in the table below.

Conversion between number systems

1.  Conversion of Decimal Numbers to Binary Numbers

When a decimal number is converted to a binary number, the decimal number can be divided by two until the remainder is 0 and the remainder of the division can be written on the right side. After that, write all the remainders from the bottom to top to build the number.

Example

Converting number 12 10 to a binary number.

First, divide this number by 2 writing the remainders.

Quotient

Converting number 12 10 to a binary number.

• First, divide this number by 2 writing the remainders

12 10 = 1100 2

2.  Converting Binary Numbers to Decimal Numbers

3.  Conversion of Decimal Numbers to Octal Numbers

Here, divide the given number by 8 until the remainder is 0 and write the remainders from bottom to top.

Example

Converting 158 10 to an octal number.

• Firstly, divide this number by 8 and write down the remainder

4.   Converting Octal Numbers to Decimal Numbers

5.  Converting Decimal Numbers to Hexadecimal Numbers

Here, divide the number by 16 until the remainder is 0 and write down the remainders from bottom to top.

Example

Converting number 38 10 to a hexadecimal number.

• Firstly, divide this number by 16 and write down the remainders.

6.  Converting Hexadecimal Numbers to Decimal Numbers

7.  Converting Binary Numbers to Octal Numbers

Converting 10111012 to an octal number.

• First, divide the number into three bits from the right corner to the left corner. If the last cluster in the left corner does not consist of 3 bits, add 0s to complete.
• Write each octal number separately for each cluster.
• Then write these clusters in octal digits.
• Write these digits in order from the left corner to the right corner.

8. Converting Binary Numbers to Hexadecimal Numbers

Converting number 101102 to a hexadecimal number.

• First, divide the number into four-bit clusters from the right corner to the left corner.
• Write hexadecimal numbers separately for each cluster.
• Write these numbers in order from the left corner to the right corner and write down the base

9.  Converting Octal numbers to Binary Numbers

Converting number 4578 to a binary number.

• Firstly, write each digit in octal number in three bits.
• Secondly, write down all the bits together to get the binary number for the octal number.

10.  Converting Octal numbers to Hexadecimal Numbers

Converting number 10578 to a hexadecimal number.

• First, write each digit in octal number in three bits.
• Divide the binary number you get into four-bit clusters from the right corner to the left corner.
• Write the related hexadecimal number for each cluster.

11.  Converting Hexadecimal Numbers to Binary Numbers

12.  Converting Hexadecimal Numbers to Octal Numbers

First, the hexadecimal number should be converted to a binary number and then it should be converted to an octal number.

Representation of decimal numbers (signed and unsigned)

Unsigned binary numbers are, by definition, positive numbers and thus do not require an arithmetic sign. An m-bit unsigned number represents all numbers in the range 0 to 2m -1. For example, the range of 8-bit unsigned binary numbers is from 0 to 255 10 in decimal and from 00 to FF 16 in hexadecimal. Similarly, the range of 16-bit unsigned binary numbers is from 0 to 65, 535 10 in decimal and from 0000 to FFFF 16 in hexadecimal.

Signed number, on the other hand, require and arithmetic sign. The most significant bit of the binary numbers is used to represent the sign bit. If the sign bit is equal to zero, the signed binary number is positive; otherwise, it is negative. The remaining bits represent the actual number. There are three ways to represent negative number.

Signed integer representations

• Signed magnitude

In the sign-magnitude representation method, a number is represented in its binary form. The most significant bit (MSB) represents the sign. A 1 in the MSB bit position denotes a negative number; a 0 denotes a positive number. The remain n-1 bits are preserved and represent the magnitude of the number. The following examples illustrate the sign-magnitude representation:

(+3) = 0011 → (-3) = 1011

(+7) = 0111 → (-7) = 1111

(+0) = 0000 → (-0) = 1000

• One’s complement

1’s complement works by swapping 1s for 0s and the 0s for 1s for example

0000 0010 (2)

Will become…

1111 1101 (-2)

Much like the sign-and-magnitude method this is easily defined as a negative number because its most significant bit is 1.

• Two’s Complement

2’s complement is a more difficult way of storing negatives. There are three steps for it:

1. Find the positive binary number (e.g. 8base 10 = 0000 1000base 2).
2. Swap the 1s for 0s and 0s for 1s (e.g. 0000 1000base2 become 1111 01111base 2).–This is known as “flipping the bits”, or applying logical NOT to the original base 2 representation.
3. Add 1 (e.g. 1111 01111base 2 + 1base 2 = 1111 1000base 2).

This method is liked because:

• It’s like sign and magnitude; a negative number starts with a 1 and a positive number starts with a 0.
• The binary arithmetic will work.
• There is only one value for 0 (0000 0000base 2).

Methods of character representation

• Binary Coded Decimal (BCD)

BCD uses 6 bits and can represent 26=64 characters. The first three bits are used as zone bits and the last three bits indicate the digit.

• American Standard Code for Information Interchange (ASCII)

ASCII-7: uses 7 bits and can represent 27=128 characters. The first three bits are used as zone bits and the last four bits indicate the digit. Hexadecimal numbers are used as shortcut notation for memory dump.

ASCII-8: uses 8 bits and can represent 28 =256 characters. For all practical purposes an 8 bit code is used.8th bit is added for parity. Characters are assigned decimal values.

• Unicode

We can quickly run into trouble as ASCII can’t possibly store these hundreds of thousands of extra characters in just 7 bits. What we use instead is Unicode. Each Unicode character can be encoded on a computer using three different standards that differ on the minimum number of bits used;

UTF-8

UTF-16

UTF-32

Though 128 characters can be used in the ASCII system and 256 characters can be used in the EBCDIC system for data representation. For example, these systems cannot be used for Sinhala, Japanese, Chinese and Tamil languages as there are more than 256 characters. Hence Unicode system was designed according to a standard to represent 65536 different symbols of 16 bits (2 16 = 65536).

Binary arithmetic operations – (integers only)

Binary arithmetic is essential part of all the digital computers and many other digital system.

Binary addition

It is key for binary subtraction, multiplication, division. There are four rules of binary addition.

Binary subtraction

Subtraction and borrow, these two words will be used very frequently for the binary subtraction. There are four rules of binary subtraction.

Logical operations

Bitwise logical operations

Bitwise logic instructions cause the values stored in two registers to be combined, bit by bit, by a logic operator.

Types of bitwise operations

• OR
• AND
• XOR
• NAND
• NOR
• NXOR

What is the process of converting information?

Is the process of converting information such as text numbers photo or music into digital data that can be manipulated by electronic devices?

Is the process of converting a photograph a song or text into digital information or bits?

What is the process of converting text numbers sound photos and video into data that can be processed by digital devices?