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

Step2: Translate the absolute values of letters to number equivalent

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

To convert hexadecimal number into binary, proceed as follows:

1> Convert individual numbers to binary

2> Combine binary digits

Example:

Convert 321₁₆ into binary

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 16² + C x 16¹ + 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.