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Unformatted text preview: igits (0 to 7) in the octal number system (refer to Figure 3.1), 3 bits (2 3 = 8) are
sufficient to represent any octal number in binary. Since decimal digits 0 to 7 are equal to
octal digits 0 to 7, binary to decimal conversion can be used in this step.
Example 3.18.
1011102 = ?8
Solution:
Step 1: Divide the binary digits into groups of 3 starting from right (LSD).
101 110
Step 2: Convert each group into one digit of octal (use binarytodecimal conversion).
1012=lx22 + 0x21 + lx2°
=4+0+1
= 58
1102= Ix22+1 x2'+0x2°
=4+2+0 = 68
Hence, 1011102 = 568
Compare the result with the result of Example 3.16.
Example 3.19.
11010102 = ?8 Solution:
1101010a =001 101 010 (Group of 3 digits from right)
= 1528 (Convert each group to an octal digit) Hence, 11010102 = 1528
Shortcut Method for Octal to Binary Conversion
The following steps are used in this method:
Step 1: Convert each octal digit to a 3 digit binary number (the octal digits may be treated
as decimal for this conversion).
Step 2: Combine all the resulting binary groups (of 3 digits each) into a single binary
number.
Example 3.20.
5628 = ?2
Solution:
Step 1: Convert each octal digit to 3 binary digits.
58=1012 68
=1102 28 = 0102
Step 2: Combine the binary groups.
5628 = 101/5 110/6 010/2
Hence, 5628 = 1011100102
Shortcut Method for Binary to Hexadecimal Conversion
The following steps are used in this method:
Step 1: Divide the binary digits into groups of four (starting from the right).
Step 2: Convert each group of four binary digits to one hexadecimal digit. Remember that
hexadecimal digits 0 to 9 are equal to decimal digits 0 to 9, and hexadecimal digits A to F
are equal to decimal values 10* to 15. "Hence for this step, the binary to decimal
conversion procedure can be used, but the decimal values 10 to 15 must be represented as
hexadecimal A to F.
Example 3.23.
101101011002 = ?16
Solution:
Step 1 : Divide the binary digits into groups of 4.
1101 0011
Step 2: Convert each group of 4 binary digits to 1 hexadecimal digit.
11012 =1 x 23 + 1 x 22 + 0 x 21 + 1 x 2°
=8+...
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 Spring '14

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