The number base converter translates numerical representations across standard positional numeral systems used in computer architecture, memory addressing, and embedded systems programming. By parsing an input string according to its source radix, the utility immediately computes the equivalent values in binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).

### Positional Radix Mathematics

A number with digits $d_k d_{k-1} \dots d_0$ in base $b$ evaluates to: $\text{Value} = \sum_{i=0}^{k} d_i \times b^i$

When converting between bases: - **Base 2 (Binary):** Fundamental bit representation for boolean logic and memory states. - **Base 8 (Octal):** Compact three-bit groupings historically common in UNIX file permissions. - **Base 10 (Decimal):** Standard human decimal arithmetic. - **Base 16 (Hexadecimal):** Compact byte representation where each hex digit represents exactly 4 bits (one nibble).

### Worked Numeric Example

Converting the decimal value **255** (source base 10): 1. **Binary (base 2):** $255 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 \rightarrow$ **`11111111`** (8 bits). 2. **Octal (base 8):** $\lfloor 255 / 64 \rfloor = 3$, remainder 63; $\lfloor 63 / 8 \rfloor = 7$, remainder 7 $\rightarrow$ **`377`**. 3. **Decimal (base 10):** **`255`**. 4. **Hexadecimal (base 16):** $255 = (15 \times 16) + 15 = \text{FF}_{16} \rightarrow$ **`FF`**.

If you change the input base to 16 and enter **`1A`**, the tool parses $(1 \times 16) + 10 = 26$ in decimal, `11010` in binary, and `32` in octal.

### Client-Side Execution Note

Parsing uses native JavaScript `parseInt(input, base)` and `Number.prototype.toString(radix)` directly inside your browser. No numeric inputs or conversion requests are sent over the network.