Convert a whole number from base 8 to its equivalent binary (base 2) representation.
Enter an integer containing only octal digits 0 through 7.
The converter accepts up to 1,000 octal digits and preserves the exact integer value. Leading zeroes are omitted from the result.
Convert a whole number written in octal (base 8) into its binary (base 2) representation. Each octal digit maps directly to exactly three bits, preserving the integer’s value.
Enter digits 0 through 7 only. The calculator supports up to 1,000 digits, preserves large values exactly, and omits unnecessary leading zeroes in the binary output.
For a manual check, replace each octal digit with a three-bit group: 0→000, 1→001, 2→010, 3→011, 4→100, 5→101, 6→110, and 7→111.
Binary = concatenate the 3-bit encoding of each octal digit, then remove leading zeroes. This works because 8 = 23.
| Term | Meaning |
|---|---|
| Octal digit | A digit from 0 through 7, each equivalent to a three-bit binary group. |
| Binary output | The concatenated bit groups with unnecessary leading zeroes removed. |
Convert octal 52:
Check both values in decimal: 5×8+2 = 42, and binary 101010 = 32+8+2 = 42.
The binary result represents the same nonnegative integer as the octal input. The output is a bit string, not a signed machine value; interpreting signed encodings would require a bit width and representation that this form does not request.
Leading zeroes are omitted because they do not change an integer’s value. Keep the original octal value beside the output if you need to document the conversion.
It replaces each octal digit with its three-bit binary equivalent and removes leading zeroes. The integer’s value is unchanged.
Only digits 0 through 7 belong in an octal number. Leading zeros do not change its numeric value.
Repeat the worked example first. For octal-to-binary converter, it should agree with this check: Octal 17 equals binary 1111 because the octal digits 1 and 7 map to 001 and 111.
It may use another definition, factor, period or rounding rule. This page has this specific limit: Only digits 0 through 7 belong in an octal number. Leading zeros do not change its numeric value.
No rounding is needed. The output is an exact bit representation of the input integer.
Zero is accepted where it has a real meaning, but the octal-to-binary converter rejects a zero divisor or another value that makes the formula undefined.
Use the octal-to-binary converter to check arithmetic. Review the underlying records and obtain suitable professional advice when the decision has serious consequences.