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Digital Number System Part-II

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Code Conversion

Converting from one code form to another code form is called code conversion, like converting from binary to decimal or converting from hexadecimal to decimal.

Binary-To-Decimal Conversion
Any binary number can be converted to its decimal equivalent simply by summing together the weights of the various positions in the binary number which contain a 1.

Binary

Decimal

110112

 

24+23+01+21+20

=16+8+0+2+1

Result

2710

and

 

Binary

Decimal

101101012

 

27+06+25+24+03+22+01+20

=128+0+32+16+0+4+0+1

Result

18110

You should have noticed that the method is to find the weights (i.e., powers of 2) for each bit position that contains a 1, and then to add them up.

Decimal-To-Binary Conversion
There are 2 methods:

  • Reverse of Binary-To-Decimal Method
  • Repeat Division

Reverse of Binary-To-Decimal Method

 

Decimal

Binary

4510

=32 + 0 + 8 + 4 +0 + 1

 

=25+0+23+22+0+20

Result

=1011012

Repeat Division-Convert decimal to binary
This method uses repeated division by 2.

Convert 2510 to binary

 

Division

Remainder

Binary

25/2

= 12+ remainder of 1

1 (Least Significant Bit)

12/2

= 6 + remainder of 0

0

6/2

= 3 + remainder of 0

0

3/2

= 1 + remainder of 1

1

1/2

= 0 + remainder of 1

1 (Most Significant Bit)

Result

2510

= 110012

The Flow chart for repeated-division method is as follows:

 

Binary-To-Octal / Octal-To-Binary Conversion

 

Octal Digit

0

1

2

3

4

5

6

7

Binary Equivalent

000

001

010

011

100

101

110

111

Each Octal digit is represented by three binary digits

 

Example

100 111 0102 = (100) (111) (010)2 = 4 7 28

Repeat Division-Convert decimal to octal
This method uses repeated division by 8.
Example
: Convert 17710 to octal and binary

Division

Result

Binary

177/8

= 22+ remainder of 1

1 (Least Significant Bit)

22/ 8

= 2 + remainder of 6

6

2 / 8

= 0 + remainder of 2

2 (Most Significant Bit)

Result

17710

= 2618

Binary

 

= 0101100012

Hexadecimal to Decimal/Decimal to Hexadecimal Conversion
Example:

2AF16 = 2 x (162) + 10 x (161) + 15 x (160) = 68710

Repeat Division- Convert decimal to hexadecimal
This method uses repeated division by 16.

Example: convert 37810 to hexadecimal and binary:

 

Division

Result

Hexadecimal

378/16

= 23+ remainder of 10

A (Least Significant Bit)23

23/16

= 1 + remainder of 7

7

1/16

= 0 + remainder of 1

1 (Most Significant Bit)

Result

37810

= 17A16

Binary

 

= 0001 0111 10102

Binary-To-Hexadecimal /Hexadecimal-To-Binary Conversion

Hexadecimal Digit

0

1

2

3

4

5

6

7

 

Binary Equivalent

0000

0001

0010

0011

0100

0101

0110

0111

 

 

Hexadecimal Digit

8

9

A

B

C

D

E

F

Binary Equivalent

1000

1001

1010

1011

1100

1101

1110

1111

Each Hexadecimal digit is represented by four bits of binary digit.

Example:

1011 0010 11112 = (1011) (0010) (1111)2 = B 2 F16

Octal-To-Hexadecimal Hexadecimal-To-Octal Conversion

  • Convert Octal (Hexadecimal) to Binary first.
  • Regroup the binary number by three bits per group starting from LSB if Octal is required.
  • Regroup the binary number by four bits per group starting from LSB if Hexadecimal is required.
    Example:
    Convert 5A816 to Octal.

Hexadecimal

Binary/Octal

5A816

0101 1010 1000 (Binary)

 

010 110 101 000 (Binary)

Result

= 2 6 5 0 (Octal)

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Lần cập nhật cuối ( Thứ ba, 29 Tháng 3 2022 00:16 )