Since decimal digits 0 to 7 are equal to octal digits

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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 binary-to-decimal 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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