Page 16 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 1: Number Systems

1.5.2 Converting from Decimal to Another Base (Division-Remainder Notes
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 1 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.

25 10
Solution:

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

Steps 5: 1/2 = 0 and remainder 1
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
1.5.3 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
Solution:
Step 1: Convert from base 6 to base 10

545 = 5*6 + 4*6 + 5*6 0
2
1
= 5*36 + 4*6 + 5*1
= 180 + 24 + 5

= 209
10

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