Binary to Octal Converter
Convert between binary and octal number systems using the 3-bit grouping technique. Essential for Unix permissions, embedded systems, and digital logic.
How do I convert binary to octal?
Binary to octal conversion uses grouping of 3 bits. Starting from the rightmost bit (or decimal point for fractions), group binary digits into sets of three. Pad with leading zeros if needed. Convert each 3-bit group to its octal equivalent using the 3-bit table: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. Example: 110101 binary → groups 110 and 101 → 65 octal. For fractions: group to the right of the decimal point, padding with trailing zeros.
How do I convert octal to binary?
Octal to binary conversion is the reverse: replace each octal digit with its 3-bit binary equivalent. Write each octal digit as a 3-bit group using the table: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. Example: 257 octal = 010 101 111 binary = 10101111 (leading zero dropped). 34.7 octal = 011 100.111 binary = 11100.111. This method works because octal (base-8) = 2^3, so each octal digit maps to exactly 3 binary bits.
Why is octal still used in computing?
Octal persists in computing for several reasons: Unix/Linux file permissions use octal (chmod 755 = rwxr-xr-x). Each octal digit maps to exactly 3 bits, making it more compact than binary but easier than hex for representing 12-, 24-, or 36-bit systems. Some older computer architectures (PDP-8, IBM System/360) used word sizes divisible by 3. Digital displays and some embedded systems still use octal for configuration. Modern usage: file permission masks (0777, 0644), ASCII representation in some contexts, and networking (IP address octets pattern).
What is the octal number system and how does it work?
Octal is a base-8 number system using digits 0-7. Each place value represents a power of 8: 8^0=1 (ones), 8^1=8 (eights), 8^2=64 (sixty-fours), 8^3=512, etc. Example: 345 octal = (3×64) + (4×8) + (5×1) = 192 + 32 + 5 = 229 decimal. Octal avoids digits 8 and 9, making it unambiguous. Counting in octal: 0,1,2,3,4,5,6,7,10,11,...17,20, etc. The number after 7 is 10 (which equals 8 decimal). This is why octal is sometimes called "base-8 notation".