CM VIII - Binary Number system - BITS and BYTES

Jyoti: How does a computer store music and audio?

Moz: Computers store all data, like information, instructions, files, images, sound and video as numbers.

Jyoti: Is there some code to represent each letter in the alphabets? This will be necessary for saving a text document.

Moz: You are right.

Tejas: To represent an image each pixel or the coloured dots need to have a code.

Jyoti: Different sounds in a music file also have to be given a code.

Moz: Yes. All the data has to be converted to numbers in binary form to be processed by the computer. The word binary means two. The binary form code is formed by using only two values '0' and '1'. This is called the binary number system.

Tejas: Why are only two digits used to form the code?

The reason computers use the base-2 system is because it makes it a lot easier to implement them with current electronic technology. Bits can be implemented in many forms. In most modern computing devices, a bit is usually represented by an electrical voltage or current pulse, or by the electrical state of a flip-flop circuit.

Examples of Binary code:

Alphabet / Binary code
A / 1000001
Z / 1011010

And

The following are binary codes of your names:

Tejas – 01010100 01100101 01101010 01100001 01110011

Jyoti - 01001010 01111001 01101111 01110100 01101001

Jyoti: 'J' (01001010) and 'j' ( 01101010) have different code to distinguish between the upper case and lowercase.

Tejas: Each letter has a length of 8 BITs.

Moz: Good observation. BITs are usually grouped into groups of 8, and each group is called a Byte.

Tejas; Oh! So when a file has a size of 1 KB then it means the file has 1000 bytes = 8000 bits.

Right. Write down the table of bits and bytes starting from Kilobytes to Terrabytes. Note that bits are abbreviated by 'b' and bytes by 'B'.

Concept: Binary numbers

A binary number is formed by the combination of '0' and '1'.

Bit

0 / 1

A bit is the smallest

unit of data in computer processing.

·  Bit is derived from the words Binary digIT.

·  A bit represents a digit in the binary system.

·  A bit can only have the value 0 or 1.

·  An example: 1101 is a binary number 4 bits long.

Byte

0 / 1 / 1 / 0 / 1 / 1 / 1 / 0

A Byte is a group of 8 bits.

·  Bytes are the standard unit of storage in a computer.

·  An example: 10110111 is a byte and can represent data like text, pixels, sound in a computer.

Units of measure:

The kibibyte is a multiple of the unit byte for quantities of digital information. The binary prefix kibi means 1024; therefore, 1 kibibyte is 1024bytes. The unit symbol for the kibibyte is KiB.

·  A Kilobyte (KB) is usually used to denote 1000 bytes. Sometimes it is used to denote 2^10 bytes or strictly 1024 bytes.

·  A Megabyte (MB) is 1024 kilobytes.

·  A gigabyte (GB) is 1,024 megabytes.

·  A terabyte (TB) is 1,024 Gigabytes.

Worksheets

1. Fill in the blanks

a)  _____ and ______are digits in the binary system.

b)  Binary numbers can represent data like ______, ______and ______in computers. ______.

c)  A Byte is a group of ___ bits.

Match the following

KB / 1024 megabytes
Byte / 1024 bytes
GB / 1024 gigabytes
MB / 1024 kilobytes
TB / 8 bits