7. Converting hexadecimal numbers into binary numbers

posted Jun 30, 2014, 9:58 PM by Maurice Nyamoti   [ updated Jul 12, 2014, 5:18 AM ]

Converting binary numbers to hexadecimal numbers

To convert binary numbers to their hexadecimal equivalents, simply group the digits of the binary number into groups of four from right to left e.g. 1101 0010. The next step is to write the hexadecimal equivalent of each group e.g.

1101       -               D

0010       -               2

The equivalent of 1101 00102 is D2H or D216:             H for hexadecimal

Converting hexadecimal numbers to decimal and binary numbers

Converting hexadecimal numbers to decimal number

To convert base 16 numbers to base 10, proceed as follows

i)                    Write  the place values starting from the right hand side

ii)                  If a digit is a letter such as an ‘A’ write its decimal equivalent

iii)                Multiply each hexadecimal digit with its corresponding place value and then add the products

Example:

Convert the hexadecimal number D8F16 to its equivalent decimal

Step1: write place values

Place value

162

161

160

Hexadecimal absolute value

D

8

F

Step2: Translate the absolute values of letters to number equivalent

Place value

162

161

160

Hexadecimal absolute value

13

8

15

A             B             C              D             E              F

10           11           12           13           14           15

Step3: Multiply and add

(162x13) + (161x8) + (160x15)

3328 + 128 + 15

3471

Therefore, D8F16 is equivalent to 347110

Converting hexadecimal numbers into decimal numbers

Hexadecimal-Decimal- Binary converter table

Hexadecimal digits

Decimal equivalents

Binary equivalent

00

00

0000

01

01

0001

02

02

0010

03

03

0011

04

04

0100

05

05

0101

06

06

0110

07

07

0111

08

08

1000

09

09

1001

A

10

1010

B

11

1011

C

12

1100

D

13

1101

E

14

1110

F

15

1111

To convert hexadecimal number into binary, proceed as follows:

1>     Convert individual numbers to binary

2>     Combine binary digits

Example:

Convert 32116 into binary

Hexadecimal digits

3

2

1

Binary equivalents

0011

0010

0001

Combining the three sets of bits, we get 0011001000012

Convert hexadecimal fraction to decimal fraction

Solved examples of octal fractions to decimal fraction conversion

Problem 1: Convert ( E  F . B 1 )16= ( ? )10
  E F .  B  1
    ↑             ↑
MSD         LSD
= E x 161 + F x 160 .  B x 16-1 + 1 x 16-2  

= 14 x 16  + 15 x 1   .  11 x ( 1 / 16 ) + 1 x ( 1 / 256 )  

=  224   +    15        .  ( 0. 6 8 7 5 )  ( 0 . 0 0 3 9 0 6 2 5 )   

=  239  +  0. 6914

=  239 . 691406

Therefore  ( E F . B 1 )16 =  ( 2 3 9  .  6 9 1 4 0 6 )10

Problem 2: Convert ( 0.9D9 )16= ( ? )10
=  0  . 9 D 9
    ↑            ↑
MSD          LSD

=  0 x 160 .  9 x 16-1 + D x 16-2  + 9 x 16-3

=  0 x 1  .  9 x ( 1 / 16 ) + 13 x ( 1 / 256 )  + 9 x ( 1 / 4096 )  

=  0  .  (0. 5625) +  (0 . 050781 )   +  ( 0. 0021972 )   

= 0  .  ( 0 . 6154782 )

0 . 6154782

Therefore  ( 0 . 9 D 9 )16 =  ( 0 . 6 1 5 4 7 8 2 )10

Problem 3: Convert ( BBC.1 0 )16= ( ? )10
=  B C  C . 1 0 
    ↑                 ↑
 MSD           LSD
= B x 16+ C x 16+ C x 160 .  1 x 16-1 + 0 x 16-2 

= 11 x 256+ 12 x 16+ 12 x 1    .  1 x ( 1 / 16 ) + 1 x ( 1 / 256 )
  
= 2816      + 192       + 12          .  ( 0 . 0625 )  ( 0 )   

= 3020   .   ( 0. 0625 )    

= 3020 . 0625

Therefore  ( B C C . 1 0 )16 =  ( 3 0 2 0 . 0 6 2 5 )10

Quiz

A.       Convert the following hexadecimal numbers into decimal numbers

1>     3216

2>     CCD16

3>     EFE16

4>     11916

5>     32816

6>     ABD16

7>     10AFFD16

8>     DDFF3416

9>     11ABDF16

10>  CDFF3116

More questions

B.       Convert the following hexadecimal numbers into binary form

i)                    29416

ii)                  24716

iii)                EFD16

iv)                90716

v)                  BAD16

vi)                CBDF16

vii)              585C16

viii)            ABCD16

ix)                 55C3A16

x)                   33111CF16

C.       Convert 1111000110111 to its hexadecimal equivalent.

Comments