ADDITIONAL JAVA TOPICS - Java Programming: From Problem Analysis to Program Design - page 953

Consider the binary number 1101100010101. To find the equivalent octal number, starting
from right to left, we consider three digits at a time and write their octal representation. Note
that the binary number 1101100010101 has only 13 digits. So when we consider three digits
atatime,attheend,wewillbeleftwithonlyonedigit.Inthiscase,wejustaddtwo0stothe
left of the binary number; the equivalent binary number is 001101100010101. Thus:

1101100010101 2 ¼ 001101100010101 2

¼ 001 101 100 010 101

¼ 15425 8 because 001 2 ¼ 1 8 , 101 2 ¼5 8 , 100 2 ¼ 4 8 , 010 2 ¼ 2 8 , and
101 2 ¼ 5 8 .
Thus, 1101100010101 2 ¼ 15425 8 .
To convert an octal number into an equivalent binary number, using Table D-1, write
the binary representation of each octal digit in the number. For example:

3761 8 ¼ 011 111 110 001 2

¼ 011111110001 2

¼ 11111110001 2 .
Thus, 3761 8 ¼ 11111110001 2 .
Next, we discuss how to convert a binary number into an equivalent hexadecimal
number and vice versa. The method to do so is similar to converting a number from
binary to octal and vice versa, except that here we work with four binary digits. Table D-
2 gives the binary representation of the first 16 hexadecimal numbers.

TABLE D-2 Binary Representation of First 16 Hexadecimal Numbers

Binary Hexadecimal Binary Hexadecimal

0000 0 1000 8

0001 1 1001 9

0010 2 1010 A

0011 3 1011 B

0100 4 1100 C

0101 5 1101 D

0110 6 1110 E

0111 7 1111 F