Question

Qυεѕтıσи!!!

ᴇxᴩʟᴀɪɴ ᴀʙᴏᴜᴛ 'ɴᴜᴍʙᴇʀ ꜱyꜱᴛᴇᴍ'

ɪ) ᴅᴇᴄɪᴍᴀʟ ɴᴜᴍʙᴇʀ ꜱyꜱᴛᴇᴍ

ɪɪ) ʙɪɴᴀʀy ɴᴜᴍʙᴇʀ ꜱyꜱᴛᴇᴍ

ɪɪɪ) ᴄᴏɴᴠᴇʀꜱɪᴏɴ ᴏꜰ ᴅᴇᴄɪᴍᴀʟ ɴᴜᴍʙᴇʀꜱ ᴛᴏ ʙɪɴᴀʀy ɴᴜᴍʙᴇʀꜱ

ɪᴠ) ᴄᴏɴᴠᴇʀꜱɪᴏɴ ᴏꜰ ʙɪɴᴀʀy ɴᴜᴍʙᴇʀꜱ ᴛᴏ ᴅᴇᴄɪᴍᴀʟ ɴᴜᴍʙᴇʀꜱ



ꜱᴜʙᴊᴇᴄᴛ:- ᴄᴏᴍᴩᴜᴛᴇʀ
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Answer 1

Aиѕωεя!!!

❶ 'ɴᴜᴍʙᴇʀ ꜱyꜱᴛᴇᴍ' :-

➙A number system is a Mathematical way to write numbers. Computer is a machine and does not understand the language that human beings speak.The instructions given to a computer can be in the form of letters or words. It translates the letters or words that you type into numbers.This is because it can understand only numbers.

A computer can understand the positional number system or place value notation,where the value of the digit depends on it's position.

The value of each digit in a number can be determined using:

➙The Digit

➙The position of the digit in the number

➙The base of the number

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❷ 'ᴅᴇᴄɪᴍᴀʟ ɴᴜᴍʙᴇʀ ꜱyꜱᴛᴇᴍ' :-

➙The decimal number system consists of digits 0-9. These 10 digits can be used in any combination to form any number.

Some examples of Decimal numbers are -

608, 1711, 571 & 2836.

The base of the decimal number is 10 because the total digits in this number system is 10.The value of each digit is based on it's position in a number.

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❸ 'ʙɪɴᴀʀy ɴᴜᴍʙᴇʀ ꜱyꜱᴛᴇᴍ' :-

➙Unlike the decimal number system, the Binary Number System has only two numbers.They are 0 & 1.

Some examples of Binary Number System are 11101 , 10111 , 1010 , etc.

The binary number system is also called as the base 2 number system. Any data and instruction

entered in a computer is converted to binary form because a computer understands only the binary language. The binary language is then converted into decimal language. In the binary number system, the number 1 means 'ON' and 0 means 'OFF'.

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❹ 'ᴄᴏɴᴠᴇʀꜱɪᴏɴ ᴏꜰ ᴅᴇᴄɪᴍᴀʟ ɴᴜᴍʙᴇʀꜱ ᴛᴏ ʙɪɴᴀʀy ɴᴜᴍʙᴇʀꜱ' :-

➙The division method is used to convert a decimal number into a binary number.

The steps are :-

• Divide the Number by 2

• Keep dividing the quotient by 2 until it becomes 0

• Write the remainders obtained in each step in the table in reverse order.

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❺ 'ᴄᴏɴᴠᴇʀꜱɪᴏɴ ᴏꜰ ʙɪɴᴀʀy ɴᴜᴍʙᴇʀꜱ ᴛᴏ ᴅᴇᴄɪᴍᴀʟ ɴᴜᴍʙᴇʀꜱ' :-

➙We use multiplication method to convert binary numbers to decimal numbers.

The steps are :-

• Multiply each digit by base 2 with it's power based on the position of the digit.

• Add the products obtained.

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Answer 2

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I) Decimal system, also called Hindu-Arabic number system or Arabic number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It also requires a dot (decimal point) to represent decimal fractions.

Ii) Binary number system, in mathematics, positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1, instead of the usual 10 different symbols needed in the decimal system

III) An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero. So for example.

IV) Since there is no binary point here and no fractional part. So, Binary to decimal is, = (11001010)2 = 1x27+1x26+0x25+0x24+1x23+0x22+1x21+0x20 = 128+64+0+0+8+0+2+0 = (202)10. Example-2 − Convert binary number 1010.1011 into decimal number

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