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Basics of Computers Number System

Basics of Computers Number System

The technique for representing numbers and working with them is called the number system. System of decimal numbers is the most common system of numbers. Other popular numbers include the system of binary numbers, the octal number system, the hexadecimal number system, etc.

Decimal Number System

Decimal number system is a series of base ten numbers containing 10 digits from 0 to 9. This means that these 10 digits can be used to represent any numerical quantity. The decimal number method is likewise a function of positional value. This implies digit values can depend on their position. To understand this let's take an example.

Say we have three numbers – 734, 971 and 207. The value of 7 in all three numbers is different−

In 734, value of 7 is 7 hundreds or 700 or 7 × 100 or 7 × 102

In 971, value of 7 is 7 tens or 70 or 7 × 10 or 7 × 101

In 207, value 0f 7 is 7 units or 7 or 7 × 1 or 7 × 100

Instructions are given in digital systems via electrical signals; variation is done by varying the signal voltage. It's difficult to implement decimal number system in digital equipment with 10 different voltages. So a number of computational structures have been developed and are simpler to execute digitally. Let's look in depth at these.

Binary Number System

Two-state method is the best way to change instructions by electrical impulses-on and off. On is defined as 1 and off as 0, while 0 at a lower voltage is not in reality a signal but a signal. The number system of only such two digits-0 and 1-is named the method of binary numbers.

Additionally, every binary digit is called a bit. Binary number system is also a positional value system, as seen here, where each digit has a value represented in powers of 2.

For every binary number the least significant bit (LSB) is considered the rightmost digit, while the most significant bit (MSB) is called the leftmost digit.

And the decimal equivalent of this number is sum of the product with its positional value of each digit.

110102 = 1×24 + 1×23 + 0×22 + 1×21 + 0×20

= 16 + 8 + 0 + 2 + 0

= 2610

Computer memory is calculated by how many bits it is able to store. Here's a memory ability conversion chart.

1 byte (B) = 8 bits

1 Kilobytes (KB) = 1024 bytes

1 Megabyte (MB) = 1024 KB

1 Gigabyte (GB) = 1024 MB

1 Terabyte (TB) = 1024 GB

1 Exabyte (EB) = 1024 PB

1 Zettabyte = 1024 EB

1 Yottabyte (YB) = 1024 ZB

Octal Number System

Octal number scheme consists of eight digits – 0 , 1, 2, 3, 4 , 5 , 6, 7. Octal number system is also a system of positional value with a value expressed in 8 powers for each digit.

Decimal equivalent to any octal number is a sum of the element with its positional value for every integer.

7268 = 7×82 + 2×81 + 6×80

= 448 + 16 + 6

= 47010

Hexadecimal Number System

There are 16 symbols in the octal number sequence – 0 to 9 and A to F where A is equal to 10, B is equal to 11, and so on until F. The hexadecimal number method is indeed a function of positional significance with each digit getting its value represented in powers of 16.

Decimal equivalent to any hexadecimal number is a sum of the product with its positional value for each digit.

27FB16 = 2×163 + 7×162 + 15×161 + 10×160

= 8192 + 1792 + 240 +10

= 1023410

ASCII

In addition to numerical data, computers must be able to handle alphabets, punctuation marks, mathematical operators, special symbols, etc. which form the full English language character set. The whole set of characters or symbols is called alphanumeric codes. Usually the full alphanumeric code comprises −

  • 26 upper case letters
  • 26 lower case letters
  • 10 digits
  • 7 punctuation marks
  • 20 to 40 special characters

Now a desktop knows numeric values only, whatever the set of numbers used. So all characters must have an alphanumeric code called the numeric comparable. American Standard Code for Information Interchange (ASCII), the most commonly known alphanumeric protocol is. ASCII is a 7-bit binary which has available codes of 128 (27).

ISCII

ISCII is Indian Script Code for the Interchange of Information. IISCII was developed to support computer-aided Indian languages. IISCI assisted language includes Devanagari, Tamil, Bangla, Gujarati, Gurmukhi, Tamil , Telugu and so on. IISCI is mostly used for government departments and a new universal encoding format named Unicode was adopted before it could catch on.

Unicode

Unicode is an international coding system intended for use with various language scripts. Each character or symbol is assigned a unique numerical value, for the most part within the ASCII framework. Each script previously had its own encoding system, which could conflict with each other.