Page 33 - DCAP101_BASIC_COMPUTER_SKILLS

Basic Computer Skills

Notes 7: 1AC =?
13 10
2
1
lAC = 1 x 13 +A x 13 +C x 13 0
13
= 1 x 169 + 10 x 13 + 12 x 1
= 311
10
Compare the result with the result obtained in Example 3

2.2.2 Converting from Decimal to Another Base (Division-Remainder
Technique)

The following steps are used to convert a base 10 (decimal) number to a number in another
base
Step 1: Divide the decimal number by the value of the new base.
Step 2: Record the remainder from Step I as the rightmost digit (least significant digit)
of the new base number.
Step 3: Divide the quotient of the previous division by the new base.
Step 4: Record the remainder from Step 3 as the next digit (to the left) of the new base
number. Repeat Steps 3 and 4, recording remainders from right to left, until the
quotient becomes zero in Step 3. Note that the last remainder, thus obtained, will
be the most significant digit of the new base number.

Steps 1 and 2: 25/2 = 12 and remainder 1
Steps 3 and 4: 12/2 = 6 and remainder 0
Steps 3 and 4: 6/2 = 3 and remainder 0
Steps 3 and 4: 3/2 = 1 and remainder I
Steps 3 and 4: 1/2 = 0 and remainder 1.

As mentioned in Steps 2 and 4, the remainders are now arranged in the
reverse order, making the first remainder the least significant digit (LSD)
and the last remainder the most significant digit (MSD).

Hence, 25 = 11001
10 2
Compare the result with the result obtained in above Example 1.
2.2.3 Converting from a Base Other Than 10 to Another Base Other
Than 10

The following steps are used to convert a number in a base other than 10, to number base
other than 10:
Step 1: Convert the original number to a base (decimal) number.

Step 2: Convert the decimal number obtained in step 1 to the new base number.

545 = ?
6 4
Step 1: Convert from base 6 to base 10
1
2
545= 5 x 6 + 4 x 6 + 5 x 6 0
= 5 x 36 + 4 x 6 + 5 x 1
= 180 +24 + 5
= 209
10

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