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Unit 2: Introduction to Data Representations

Step 2: Convert 209 to base 4 Notes
10
4 209 Remainder
52 1

13 0
3 1
0 3

209 = 3101
10 4
Therefore, 545 =209 =3101
6 10 4
Hence, 546 =3101
6 4
Above example illustrates the method of converting a binary number to an octal number.
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 digit to one octal digit. Since there are only 8
3
digits (0 to 7) in octal number system, 3 bits (2 = 8) are sufficient to represent any octal
number in binary to decimal conversion method in this step.

101110 =?
2 8
Step 1: Divide the binary digits into groups of 3, starting the right (LSD).
101 110
Step 2: Convert each group into one digit of octal (use binary- to- decimal
conversion method).

1
2
1
2
101 = 1 x 2 + 0 x 2 + 1 x 2 0 110 = 1 x 2 +1 x 2 + 0 x 2 0
2 2
= 4 + 0 + 1 4 + 2 + 0
= 5 6
8 8
Hence, 101110 = 56
2 8
2.2.4 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 numbers for this conversion).
Step 2: Combine all the resulting binary groups (of 3 digits each) into a single binary
number.

562 = ?
8 2
Step 1: Convert each octal digit to 3 Binary digits.
5 = 101
8 2
6 = 110
8 2
2 – 010
8 2

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