NUMBER SYSTEM AND OPERATION

Conversion of binary, decimal, hexadecimal

A number system is a basic symbol to represent a set of quantities. They are many type of number system. Here we only focus on the decimal, hexadecimal and binary number.

Decimal Number

·         Base of 10.

·         The value is composed by 10 digit starting from 0 until 9.

Binary Number

·         Base of 2.

·         The number consists only two digit 0 and 1 only.

Hexadecimal Number

·         Base of 16.

·         The composed number start from 0 until F.

·         The number is suitable to present in fours bit number.

    

    Number System Conversion

Formula for Whole Number

Whould Number

Example 1.0

Convert decimal number to binary number.

a) 50

                                                                       50 = 110010

b) 40

Example  1.1

Covert binary number to decimal number.

Example 2.0

Covert decimal number to hexadecimal number.

Read the answer from below  to top.

Example 2.1

Covert hexadecimal number to decimal number.

Example 3.0

To convert  hexadecimal   to binary , we must convert hexadecimal number to decimal number first, then covert it to binary number.

Covert hexadecimal number to binary number.

Step 1:

Convert hexadecimal number to decimal:

Step 2:

Convert decimal number to binary number:

 Example 3.1

Covert binary number to hexadecimal number.

Step 1:

Convert binary number to decimal number:

Step 2:

Convert decimal number to hexadecimal number:

Formula for Decimal Point

Example 4.0

Convert decimal number to binary number :

Step 1:

First, draw the table and  fill in the table with weight (1 ) and value represented (2).

Step 2 :

You have to test value represented one by one. For example, can  40 minus with 32. If can,  put number  1  at binary column. If cannot ( the operation produces negative number), put 0 at the binary column. Do the same step at 0.875.

Example 4.1

Convert binary number to decimal number :

Step 1 :

Put the binary number into the binary column. Circle the value represented if the value in the binary column is 1. 

    

Step 2 :

Add the value that has been circle.

                      32 + 8 = 40                                                          0.5 + 0.25 + 0.125 = 0

Example 5.0

Convert decimal number to hexadecimal number   :

Step 1 :

 You have to test value represented one by one. For example, can  51 minus with 32. If can,  put number  1  at binary column. If cannot ( the operation produces negative number), put 0 at the binary column. Do the same step at 0.3125.

Step  2:

The binary number  divide into 4 digit. As shown in figure below.

Example 5.1

Convert hexadecimal number to decimal number   :

Step 1 :

Convert  hexadecimal to binary , you can take from number system conversion table.

Post by Nur Amelina Binti Hassan B031310041