Lesson 6, Topic 2
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Hexadecimal Numbers To Decimal Numbers Conversion

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The conversion of hexadecimal numbers to decimal numbers will involve the following.

(a) Get the last digit of the hex number

(b) Make a variable and call power

(c) Multiply the current digit with (16^power), store the result.

(d) Increment power by 1

(e) Set the current digit to the previous digit of the hex number

(f) Repeat from step 3 until all digits have been multiplies

(g) Sum the results of step 3 to get the answer.

Convert the number 1214 hexadecimal to decimal ie 121416 to base 10.

Start from the last digit of the number to convert 1214. Note that the power of zero of any number is always 1.

13                22                11                40

1 x (163) = 16 x 16 x 16 = 4096

2 x (162) =2 x 16 x 16 = 512

1x (161) = 1 x 16 =16

4 x (16o) = 4 x 1 = 4

The answer is (4 + 16 + 512 + 4096) = 462810

Convert 60116 to base 10

6 x (162) + 0 x (161) + 1 x (16o)

6 x (256) + 0 x (16) + 0 x (16)

1536 + 0 + 1 = 153710

164 163 162 161 160

164 –          16 x 16 x 16 x 16 = 65536

163 –          16 x 16 x 16       = 4096

162 –          16 x 16              =  256

161 –          16                     =    16

160 –          1                       =    1

More Examples:

4         A            D

4         10           13

=     (4 x 162)       +                  (10 x 161)       +                (13X160)

=      (4 x 256)        +                  (10 x 16)           +                (13 x 1)

=        1024          +                    160               +                13       =      1197 