(r – 1) ’s compliment: (M – N) r This is similar to r’s compliment. There is a difference while dealing with the final carry we get If we have both M & N positives, then The Procedure for doing subtraction using (r – 1) ’s compliment is as follow: Take (r – 1) ’s compliment […]

# Number System

## Subtraction using compliments

Subtraction method mentioned earlier looks good when we do it on paper and pencil but to implement a subtraction method on a digital platform then subtraction using compliments is better and efficient. r’s compliment: If we are given numbers M & N with base r, then we can to have to find M – N […]

## 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 […]

## 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 […]

## SUBTRACTION (without using compliment method)

Decimal system: Let’s now analyze the subtraction of decimal systems. For subtraction we first subtract the least significant digit of subtrahend from that of minuend and if least significant digit of subtrahend is greater than that of minuend then we take borrow from the next digit of minuend and add 10 (base) to the previous digit […]

## 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 […]

## Binary to octal & hexadecimal And Vice-versa

Binary to octal and hexadecimal: 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 […]

## 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 […]

## 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 […]

## 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 […]