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Convert integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — built for programmers debugging memory addresses, bitmasks, and hex colors.
Utility
Generated on May 23, 2026
Convert integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — built for programmers debugging memory addresses, bitmasks, and hex colors.
A base converter translates integer numbers between positional numeral systems — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each system expresses the same underlying value using different digits and place values. This tool is essential for programmers working with memory addresses and bitmasks, electronics engineers reading logic levels, computer-science students learning number theory, and web designers decoding hex colors.
Formula
Value = Σ(digit × base^position), with positions counted from 0 on the right. To convert, first parse to decimal, then repeatedly divide by the target base and collect remainders.It's 2am, you're a Karachi backend developer staring at a stack trace that includes a memory address like 0x7FFFFA88E2C0, and you're trying to figure out roughly where in memory that lives. Or you're debugging a bitmask permission flag — the API returns 0b10110101 and you need to know what that means in decimal so you can grep the docs. Or you're a CS undergrad doing the binary-to-hex conversion homework that every CS101 course assigns by tradition. This converter does instant translation between binary, octal, decimal, and hexadecimal — type into any one field, the other three update live. Hex is the workhorse for any low-level work because one hex digit equals exactly 4 bits (half a byte), so a byte fits in two hex digits and a 32-bit integer fits in eight. That alignment is why memory addresses, RGB color codes, and bitwise flags are universally written in hex — binary is too verbose, decimal doesn't align to byte boundaries. Octal mostly survives in one place: Unix file permissions (chmod 755 means owner rwx, group rx, others rx — that 7 is 111 in binary, 5 is 101). Knowing this stops you from memorizing chmod combinations as magic numbers. Worth knowing: 255 (one byte's max), 65,535 (two bytes), and 16,777,215 (three bytes = max RGB color) come up often enough that recognizing them in any base saves debugging time.
A base converter translates integer numbers between positional numeral systems — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each system expresses the same underlying value using different digits and place values. This tool is essential for programmers working with memory addresses and bitmasks, electronics engineers reading logic levels, computer-science students learning number theory, and web designers decoding hex colors. It handles any value between the supported bases and lets you see all four representations at once.
In any positional system, each digit is multiplied by its base raised to the power of its position, and the products are summed. The rightmost digit is position 0, the next is position 1, and so on. To move between bases, the calculator parses the input into a single decimal value, then repeatedly divides by the target base — the remainders at each step become the target-base digits, read from bottom to top.
Common integer values in the 4 most-used number bases — essential for programming and computer science.
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 100 | 1100100 | 144 | 64 |
| 128 | 10000000 | 200 | 80 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
| 1024 | 10000000000 | 2000 | 400 |
| 65535 | — | 177777 | FFFF |
| 16777215 | — | — | FFFFFF |
255 (FF hex) = one byte's maximum value — the cap for each RGB channel in a web color.
65,535 (FFFF hex) = max 16-bit unsigned integer — the original Internet port number range.
16,777,215 (FFFFFF hex) = max 24-bit color = pure white #FFFFFF.
Unix file permissions (chmod 755) use octal: 7 = rwx (read+write+execute), 5 = r-x.
255 in decimal equals FF in hex, 11111111 in binary, and 377 in octal — the maximum value of a single byte.
1024 in decimal equals 400 in hex and 10000000000 in binary — 2^10, the classic computing boundary.
Hex color #FF0000 equals RGB (255, 0, 0), which is pure red — each hex pair represents one 0-255 color channel.
Binary 1010 equals decimal 10 — a small illustrative example useful for teaching.
Memory address 0x7FFFFF in hex equals 8,388,607 in decimal — useful when debugging low-level code or embedded systems.
Unicode code point U+1F600 (the grinning face emoji) is hex 1F600 = decimal 128,512 — used when working with character encoding.
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