Number Base Converter

Computers store integers in binary (base 2), but humans read decimal (base 10). Programmers also use octal (base 8) and hexadecimal (base 16) because they compress long bit patterns into shorter strings. Together, binary decimal octal hexadecimal cover nearly every integer conversion task in CS courses, embedded firmware, and debugging.

Each system uses positional notation: the value of a number is the sum of each digit multiplied by the base raised to that digit's position. This number base converter accepts input in any of the four bases and displays all equivalents instantly — including very large integers via BigInt.

Conversion of number system values always passes through a common reference. The standard approach: convert the source number to decimal (or directly to binary), then convert to the target base. Because 8 = 2³ and 16 = 2⁴, octal and hex align cleanly with binary groupings:

• One octal digit = exactly 3 binary bits
• One hex digit = exactly 4 binary bits

That is why binary to octal conversion and hexadecimal to octal conversion are fast by grouping — and why a unified calculator that shows all four bases at once saves manual steps.

To perform decimal to octal conversion, repeatedly divide the decimal number by 8 and record remainders from bottom to top. Example: 255 ÷ 8 = 31 r 7; 31 ÷ 8 = 3 r 7; 3 ÷ 8 = 0 r 3 → octal 377.

Use this page as a decimal to octal calculator or decimal to octal conversion calculator: select Decimal as input base, type your number, read the Octal row. The same flow covers conversion of decimal to octal for any integer — homework checks, permission masks, or Unix file mode inspection.

Decimal to octal conversion examples:

• 8₁₀ = 10₈ (one eight, zero ones)
• 64₁₀ = 100₈
• 255₁₀ = 377₈
• 4096₁₀ = 10000₈

Octal to decimal multiplies each digit by 8 raised to its position and sums the results. Octal 377 = 3×8² + 7×8¹ + 7×8⁰ = 192 + 56 + 7 = 255.

An octal to decimal calculator avoids arithmetic errors on long numbers. Select Octal as input, enter 377, and the Decimal field shows 255 alongside binary and hex. Unix file permissions (e.g. 755) are octal literals — converting them explains why 7 means rwx for the owner.

Binary to octal groups bits from the right in threes, padding the left with zeros if needed. Binary 111 111 111 → each group 111 = 7 → octal 777. For 11111111 (8 bits): 011 111 111 → 377.

A binary to octal calculator automates grouping. Select Binary, enter 11111111, read Octal 377. Every binary to octal conversion can also route through decimal — the results match when done correctly.

Example: 1010₂ → pad to 001 010 → 12₈ = 10₁₀. Verify in the tool by switching input bases.

Octal to binary expands each octal digit to three bits. Octal 5 → binary 101. Octal 12 → 001 010 → 1010 (drop leading zeros for display: 1010).

An octal to binary calculator is essential when reading legacy Unix documentation or PDP-era dumps where addresses appear in octal. Enter octal in the input field and copy the Binary output — prefixes like 0b are shown for clarity.

Octal 10₈ = 001 000₂ = 8₁₀. Octal 377 = 111 111 111 = 255 decimal = 0xFF hex — one number, four views.

Hexadecimal to octal often converts through binary: each hex digit → 4 bits, regroup bits in threes, read octal. Hex FF → 1111 1111 → 111 111 111 → 377 octal.

Hexadecimal to octal conversion appears in memory dumps, color channel math, and assembly listings. Rather than manual regrouping, select Hexadecimal as input — the Octal row updates with every keystroke. Hex 0x1000 → octal 10000 → decimal 4096.

Hex uses digits 0–9 and A–F (10–15). Invalid characters for a base are rejected with an inline error so you catch typos before submitting homework or code reviews.

C / Java / JavaScript: 0x prefix for hex, 0b for binary (ES6+), 0o for octal. Python accepts 0o377 for octal literals.

Debugging: Register values in hex, network masks in decimal, file modes in octal — one converter bridges all representations during incident response.

This tool handles integers only (no fractions). Negative values use a leading minus sign. For numbers beyond JavaScript's safe integer limit, BigInt formatting keeps precision on output. All conversion runs locally — nothing is sent to a server.