Convert Octal to Decimal
755 in octal is 493 in decimal, so converting octal to decimal changes the digits and nothing else: both are the same quantity, 493.
In decimal
- In binary
- 111101101
- In octal The value as entered.
- 755
- In decimal
- 493
- In hexadecimal
- 1ed
- Grouped Binary in nibbles of four and hex in bytes of two, which is how both are actually read. Each hex digit is exactly four binary digits, so the two groupings line up. That correspondence is the whole reason hexadecimal exists.
- 1 1110 1101 | 1 ed
- Fits in Unsigned. A value needing more than 53 bits cannot be held exactly in a JavaScript number, which is why this converter works in BigInt. A float-based converter is silently wrong in the last digits above that.
- 16 bits
- Two's complement (16-bit) For a non-negative value this is just the padded binary form. The representation only diverges below zero.
- 0000 0001 1110 1101
- As a character Read as a Unicode code point. This is the 'binary to text' conversion, one character at a time: 65 is A, 97 is a, and the 32 between them is why setting the sixth bit changes case in ASCII.
- U+01ED ǭ
How the Number Base Converter works
755 in octal is 493 in decimal. Both spellings describe the same quantity, 493, and the conversion changes nothing except how it is written.
Every base works the same way: a digit's worth is the base times the worth of the digit to its right. In octal each position is 8 times the last, so 755 reads as 7x8^2 + 5x8^1 + 5x8^0, which comes to 493.
Octal survives in exactly one place most people meet: Unix file permissions. Three bits is read, write and execute, and three such groups cover owner, group and others. That is why 755 means rwxr-xr-x and 644 means rw-r--r--. Each octal digit is three binary digits, so 7 is 111 and 5 is 101. The other legacy is a trap rather than a use: in C and several languages descended from it, a leading zero means octal, so 010 is 8 and not 10.
In binary the same value is 1 1110 1101, which is where both of these bases ultimately resolve. Everything a machine stores is bits, and every other base here is a way of writing them that a person can hold in their head.
One limit worth knowing about converters generally. A value above 2^53 cannot be held exactly in a floating-point number, and most online converters are built on them, so a 64-bit hash or identifier comes back with its last digits silently wrong. This converter uses arbitrary-precision integers, so the conversion is exact at any size.
Number Base Converter FAQ
What is 755 in decimal?
493. In decimal that is 493, and in the other two bases 111101101 and 755.
How do I convert octal to decimal by hand?
Octal survives in exactly one place most people meet: Unix file permissions. Three bits is read, write and execute, and three such groups cover owner, group and others. That is why 755 means rwxr-xr-x and 644 means rw-r--r--. Each octal digit is three binary digits, so 7 is 111 and 5 is 101. The other legacy is a trap rather than a use: in C and several languages descended from it, a leading zero means octal, so 010 is 8 and not 10.
Why does this matter outside programming?
Mostly it does not, but two cases leak out. CSS colors are hexadecimal, so anyone adjusting a shade by hand is doing this conversion. And file permissions on any Unix machine are octal, which is why chmod takes numbers like 755.
Will this be exact for very large numbers?
Yes. The arithmetic here is arbitrary-precision, so there is no point at which digits start being approximated. Converters built on ordinary floating-point numbers lose exactness above 2^53, which 64-bit identifiers routinely exceed.