Number System

Number System:

Number System

Number System:

Number System When humans are speaking to one another, they speak in a particular language. This language is made of words and letters. Although we type words and letters in the computer, the computer does not understand the words and letters. Rather, those words and letters are translated into numbers. Computers “talk” and understand in numbers.

Types of number system:

Types of number system There are of four types of number system 1 Decimal 2 Binary 3 O ctal 4 H exadecimal

Decimal Number System:

Decimal Number System The decimal number system is the system that is commonly known with people because it is most frequently used in arithmetic and in everyday life. The decimal number system is also known as the base-10 number system.

Binary Number System :

Binary Number System The binary number system is the most basic number system that most machines (and electrical devices) use to communicate. The binary number system is also known as the base-2 number system. It uses the digits 0 and 1.

Octal Number System:

Octal Number System The octal number system, is the base -8 number system It uses the digits 0 to 7.

Hexadecimal Number System:

Hexadecimal Number System The hexadecimal number system is used as an intermediary system in computers, such as a representation of memory addresses or a representation of colors. The hexadecimal number system is also known as the base-16 number system. It uses the digits 0-9 and then A-F.

Decimal to binary, octal and hexadecimal:

Decimal to binary, octal and hexadecimal To convert decimal to binary, take LCM of number with 2. for eg (12) 10 (1100) 2 To convert decimal to octal, take LCM of number with 8. For eg (32) 10 (40) 8 To convert decimal to hexadecimal, take LCM with 16. for eg (428) 10 (1AC) 16

Shortcut Method:

Shortcut Method Can change from binary to octal by making pair of 3 and hexadecimal by making pair of 4. Binary to octal (10101) 2 , 010=2, 101=5 (25) 8 Binary to hexadecimal (10101)2, 0001=1, 0101=5 (15) 16

Binary, octal n hexadecimal to decimal:

Binary, octal n hexadecimal to decimal Binary to decimal, (101010) 2 (?) 10 = 1*2 5 +0*2 4 +1*2 3 +0*2 2 +1*2 1 +0*2 0 = (42) 10 Octal to decimal (4706) 8 (2502) 10 Hexadecimal to decimal, (2BE) 16 (702) 10

Addition:

Addition 0 0 0 0 1 1 1 0 1 1 1 10= 1 will be carried

Simple Subtraction:

Simple Subtraction 0 0 0 1 1 0 1 0 1 0 1 1

Complementary method:

Complementary method First complement 7 from 10 10=1010 7=0111=comp 1000 =1010+1000=0011=3 Second complement 12 from 19 12=1100 19=10011= 1 st comp 01100 1100+1100=11000= 2 nd comp - 00111

For decimal numbers:

For decimal numbers (110.101) 2 = (6.625) 10 Product method: (6.625)10 6.625 (6.625) 8 =(6.5) 10 Product Method Normal Method

Thank you:

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