NUMBER SYSTEM CONVERSION

In this post we will focused on the number system conversion of decimal,binary and hexadecimal only.There are many converting method that we can use to convert a number by using base 2,10 and 16.

2.1 Convert decimal number to binary number

To convert a decimal number into a binary number, you should carry out successive divisions by 2 and use the reminders of the successive divisions. 

Example:Convert a decimal number 40.3470₁₀ to a binary number

Firstly you should divide the number in two parts like this:

40.3470=40 and 0.347

Then,divide the number 40 with base 2 and multiply 0.3470 with base 2 as shown:

2.2 Convert binary number to decimal number

To convert a binary number into a decimal number,you should multiply with 
base 2.

Example:Convert a binary number 101112₂ to a decimal number

You should multiply the binary number with base 2 as shown:

2.3 Convert decimal number to hexadecimal number

To convert a decimal number into a hexadecimal number, you should carry out successive divisions by base 16 and use the reminders of the successive divisions. 

Example:Convert a decimal number 1850₁₀  to hexadecimal

You should divide the number with base 16 as shown:

2.4 Convert hexadecimal number to decimal number

To convert a hexadecimal number into a decimal number, you should multiply the number with base 16.

Example: Convert a hexadecimal number 5A0D₁₆  to decimal

You should multiply the number with base 16 as shown:

2.5 Convert binary number to hexadecimal number

To convert binary number into a hexadecimal number, you should multiply the number with base 2.

Example: Convert a binary number 11101001.0111₂  to hexadecimal

You should multiply the number with base 2 as shown:

2.6 Convert hexadecimal number to binary number

To convert a hexadecimal number into a binary number, you should carry out successive divisions by 2 and use the reminders of the successive divisions. 

Example:Convert a hexadecimal number E08B6₁₆ to binary number

You should divide the number with the base 2 as shown:

2’S COMPLEMENT NUMBER

What is a 2’s complement number?

Property

Two's complement representation allows the use of binary arithmetic operations on signed integers, yielding the correct 2's complement results.

Positive Numbers

Positive 2's complement numbers are represented as the simple binary.

Negative Numbers

Negative 2's complement numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero.

3.1 CALCULATION OF 2’S COMPLEMENT

To calculate the 2's complement of an integer, invert the binary equivalent of the number by changing all of the ones to zeroes and all of the zeroes to ones (also called 1's complement), and then add one.

Example:

3.2 TWO POSITIVE NUMBERS

When adding two positive numbers there is no need to do 1’s complement number and 2’s complement number.You just do like usual of binary addition as shown below.

EXAMPLE:

3.3 POSITIVE NUMBER AND SMALLER NEGATIVE NUMBER

When there is a negative number you should do 1’s complement number which is converting the ones to zeroes and zeroes to ones.Then add 1 which is 2’s complement number as shown below.

EXAMPLE:

NUR LIYANA BT ROSLAN

B031310295