This computer science and mathematical calculator performs arithmetic addition and bitwise logic operations on base-2 binary strings. Software engineers debugging embedded firmware, students studying digital logic design, and network administrators calculating subnet masks can evaluate binary operations alongside synchronized decimal and hexadecimal conversions.

### Supported Operations and Bitwise Logic The calculation engine supports arithmetic and fundamental Boolean logic gates:

- **Binary Addition (+):** Evaluates arithmetic sum with binary carry propagation: $$\text{Sum} = A_2 + B_2$$ - **Bitwise AND (&):** Outputs a 1 bit only when corresponding bits in both operands are 1. Useful for masking bitflags. - **Bitwise OR (|):** Outputs a 1 bit when either corresponding bit is 1. Useful for setting bitflags. - **Bitwise XOR (^):** Outputs a 1 bit when corresponding bits differ ($1 \oplus 0 = 1$, $1 \oplus 1 = 0$). Useful for cryptographic parity and checksum toggling.

### Worked Numeric Example Suppose an engineer adds two 6-bit binary registers: - **Binary Number 1 ($A$):** `101010` (decimal $42$, hex `0x2A`) - **Operation:** Addition ($+$) - **Binary Number 2 ($B$):** `010101` (decimal $21$, hex `0x15`)

**Evaluation Steps:** 1. **Decimal Conversion:** $A = 32 + 8 + 2 = 42$; $B = 16 + 4 + 1 = 21$. 2. **Arithmetic Addition:** $42 + 21 = 63$. 3. **Binary Encoding:** $63_{10} = \mathbf{111111_2}$. 4. **Hexadecimal Output:** Decimal $63$ evaluates to **`0x3F`**. 5. **Bitwise Alternative:** If evaluated with bitwise XOR ($101010 \oplus 010101$), each bit position has opposite bits, also yielding `111111` ($63$).

### Client-Side Execution Guarantee All base conversions and bitwise manipulations execute directly in local browser memory via JavaScript `parseInt(bin, 2)` and native bitwise operators. Bitstrings never transmit across any network.