Page 29 - Handout Digital Electronics

Example

Convert 110100110012 to octal number system
011 010 011 001
011 = 3; 010 = 2; 011 = 3; 001= 1
Thus 110100110012 is equivalent to 32318

1.13 Converting binary numbers to hexadecimal number system

The same steps used to convert binary numbers to octal number system apply except that instead of
diving the binary bits into groups of three, subdivide them into groups of four (4).

Steps

1. Write down the binary number
2. Divide the binary bits into groups of four bits starting from the least significant bit
3. If the number of bits to the left most bit is less than four bits, then add zero(s)
4. Convert the groups of four bits each to decimal
5. Put together the converted groups and this gives the hexadecimal number

Example

Convert 110100110012 to hexadecimal number system
0110 1001 1001
0110 = 6; 1001 = 9; 1001 = 9
So, 110100110012 = 69916

Activity

1 Consider the following numbers on different basis:

• 6210 and 628 – which of the two numbers is larger in value
• Why is it necessary to know the computer number base systems?

2 How would you quickly convert the following numbers base 10 numbers to bases 2, 8 and 16:

(i) 25610,

(ii) 280 10

3 Is it possible to use the binary exponential placeholders when converting decimal numbers to octal or
hexadecimal equivalents?

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