Hexadecimal Conversion Methods: Octal to Hexadecimal & Binary to Octal and Hexadecimal
Learn about converting octal numbers to hexadecimal using different methods, including converting to decimal first and converting binary to hexadecimal. Explore practice questions and examples for better understanding. Also, find out how to convert hexadecimal numbers to octal effortlessly.
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Presentation Transcript
Octal to Hexadecimal Number System Method 1: Hexadecimal number consist of numbers and alphabets. It is represented with base 16. The numbers from 0-9 are represented in the usual form, but from 10 to 15, it is denoted as A, B, C, D, E, F. Conversion of the octal number to hexadecimal requires two steps. First, convert octal number to decimal number. Then, convert decimal number to hexadecimal number.
Octal to decimal Example: Suppose 2158is an octal number, then it s decimal form will be, 2158= 2 82+ 1 81+ 5 80 = 2 64+ 1 8 + 5 1 = 128 + 8 + 5 = 14110
Octal to Hexadecimal Example:(141)10= (?)16 Now, convert (141)10into a hexadecimal number by dividing 141 by 16 until you get remainder less than 16. 16 141 16 8 13---D 0 8 2158= 14110 =8D16
Octal to hexadecimal Method2: When converting from octal to hexadecimal, first convert the octal number into binary and then from binary into hexadecimal. For example, to convert 215 octal into hex: octal 215 binary 010 001 101 =010001101 hexadecimal 1000 1101 =8D Drop any leading zeros or pad with leading zeros to get groups of four binary digits (bits)
Binary to Octal Binary 000 001 010 011 100 101 110 111 Octal 0 1 2 3 4 5 6 7 Binary to Hexadecimal Binary 0000 0001 0010 0011 0100 0101 0110 0111 Hexadeci mal 0 1 2 3 4 5 6 7 Binary 1000 1001 1010 1011 1100 1101 1110 1111 Hexadeci mal 8 9 A B C D E F
Practice Questions Convert the following octal numbers into hexadecimal equivalent 558 2578 3368 358
Method 1 Example: Convert 1BC16into an octal number. Solution: Given, 1BC16is a hexadecimal number. 1 0001, B 1011, C 1100 Now group them from right to left, each having 3 digits. 000, 110, 111, 100 000 0, 110 6, 111 7, 100 4 Hence, 1BC16= 6748
Hexadecimal to Octal Questions Method 1 Method 2 Q.1: Find the equivalent octal form of C116. Solution: Given, a hexadecimal number is C1 C116= (C 161) + (1 160) = C 16 + 1 1 =12 16 + 1 = 192 + 1 C116=193 (Decimal form) Now we have to convert this decimal to octal number; C116 C 1 =1100 0001 =011 000 001 = 3 0 1 =3018 The octal number is 3018 Hence, C116= 3018
Q.2: Find the equivalent octal form of F16. Solution: Given, a hexadecimal number is F. F16= (F 160) = F 1 = F = 15(Decimal form) Now we have to convert this decimal to equivalent octal number; Method 2 F16 F =1111 =1 111 =1 7 =178 The octal number is 178 Hence, F16= 178
Q.3: Find the equivalent octal form of 10516 Solution: Given, a hexadecimal number is 105. 10516= (1 162) + (0 161) + (5 160) = 1 256 + 0 16 + 5 1 =256 + 0 +5 = 261(Decimal form) Now we have to convert this decimal to equivalent octal; Method 2 10516 1 0 5 =0001 0000 0101 = 000 100 000 101 = 0 4 0 5 =4058 The octal number is 4058 Hence, 10516= 4058
Practice Questions Convert ABCD16to equivalent octal form. Convert 91216to equivalent octal form. Convert 216to equivalent octal form. Convert 1016to equivalent octal form.
