This preview shows page 1. Sign up to view the full content.
Unformatted text preview: he 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 divide 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
(MSD) of the new base number.
Example 3.8.
2510 = ?2
Solution:
Steps 1 and 2:
Steps 3 and 4:
Steps 3 and 4:
Steps 3 and 4:
Steps 3 and 4: 25/2 = 12 ahd remainder 1
12/2= 6 and remainder 0
6/2 = 3 and remainder 0
3/2 = 1 and remainder 1
1/2= 0 and remainder 1 As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so
that the first remainder becomes the least significant digit (LSD) and the last remainder
becomes the most significant digit (MSD).
Hence, 2510= 110012
Compare the result with Example 3.1.
Converting from a Base Other Than 10 to a Base Other Than 10
The following two steps are used to convert a number from a base other than 10 to a base
other than 10:
Step 1: Convert the original number to a decimal number (base 10).
Step 2: Convert the decimal number so obtained to the new base number.
Example 3.15.
5455 = ?4
Solution:
Step 1: Convert from base 6 to base 10
545 = 5 x 62 + 4 x 61 + 5 x 6°
=5x36+4x6+5x1
= 180 + 24 + 5
= 20910
Example 3.16 illustrates the method of converting a number from binary to octal.
Similarly, Example 3.17 shows how to convert a number from binary to hexadecimal.
However, these are lengthy procedures and shortcut methods can be used when we desire
such conversions. These shortcut methods are described below. Shortcut Method for Binary to Octal Conversion
The following steps are used in this method:
Step 1: Divide the binary digits into groups of three (starting from the right).
Step 2: Convert each group of three binary digits to one octal digit. Since there are only 8
d...
View
Full
Document
This document was uploaded on 04/07/2014.
 Spring '14

Click to edit the document details