Number System

COMPLIMENTS

For a number system with base r (with r > 1), there are two types of compliments: r’s compliment (r-1) ‘s compliment r’s Compliment: If we have a positive number N with integer part of n digits  then we define r’s compliment  as   10’s compliment of number (5432) 10 is 104– 5432 = 10000 – 5432 = (4568) 10           […]

Number System

MULTIPLICATION & DIVISION

We similarly can apply the procedures of addition or subtraction during multiplication and division and get the results for multiplication and division of different numbering systems MULTIPLICATION: Procedure of multiplication is same as that of decimal Generalized multiplication of two 4-digit numbers is as follow: Eg.  910 * 810 910= 10012 810 =10002 Similarly we can do it […]

Number System

ADDITION

Decimal system: Although all of us are doing addition in decimal system since years and this may look a bit odd to study this again but I’ll still emphasize to study it further. Let us analyze the addition for decimal system.  For addition we firstly add least significant digits and keep the least significant digit of […]

Number System

Decimal to hexadecimal conversion

Decimal to Hexadecimal: following the same procedure Convert 26 decimal to hexadecimal: This method is also called Hex-dabble method. Convert 0.3875 to hexadecimal We can convert a fraction from a decimal to hexadecimal form by multiplying wit base and following the same procedure. Fraction is 0.3875 0.3875 * 16                          =6.2000                =6 + 0.2000         a-1=6 0.2000 * 16                          =3.2000                =3 […]

Number System

Binary to octal conversion

To convert the number from binary to octal we make groups of 3 bits starting from the decimal point (in case of fractions)  and from right most bit (in case of integers) and write the corresponding octal equivalent of those 3 bits every time. The process of replacing the long strings of 1 & o […]

Number System

Decimal to Hexadecimal conversion

Following the same procedure as earlier Convert 26 decimal to hexadecimal: This method is also called Hex-dabble method. Convert 0.3875 to hexadecimal We can convert a fraction from a decimal to hexadecimal form by multiplying wit base and following the same procedure. Fraction is 0.3875 0.3875 * 16                          =6.2000                =6 + 0.2000         a-1=6 0.2000 * 16                          =3.2000                =3 […]

Number System

Decimal to Octal conversion

Let the decimal number be 26 so we can convert it to octal by dividing the number with the base=8  and then write the quotient and remainder as shown below and then again divide the quotient with the base till we get quotient as zero. This method is also called Oct-dabble method. Conversion of fraction from decimal […]

Number System

Binary system

This is number system which is used to represent values in the digital environment. Here value of b=2 (11101.01)2 =1*24 + 1 *23 + 1 * 22 + 0 *21 + 1 * 20+ 0 *2-1 + 1 * 2-2 = (29.25)10 so number given is equal to 29 in decimal. Representing large values in binary system may be very cumbersome […]