Page 17 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes Step 2: Convert 209 to base 4
10
Remainder
4 209 1
52 0
13
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.
1.5.4 Short-cut 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 digits
(0 to 7) in octal number system, 3 bits (2 = 8) are sufficient to represent any octal number
3
in binary to decimal conversion method in this step.

101110 = ?
2 8
Solution:
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).

101 = 1*2 + 0*2 + 1*2 0 110 = 1*2 + 1*2 + 0*2 0
2
1
2
1
2 2
= 4 + 0 + 1 4 + 2 + 0
= 5 6
8 8
Hence, 101110 = 56
2 8
Always check that analogs method is used to convert fractions while conversion
of number representations.

1.5.5 Short-cut 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.

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