Binary Addition Calculator with Step-by-Step Visualization
Perform binary addition with step-by-step carry visualization. Ideal for Computer Science students to learn bitwise operations, full adders, and logic gates. Supports large integers.
Step-by-Step Operation
About
Binary addition is the fundamental operation powering every modern central processing unit (CPU). Unlike the decimal system, which uses ten digits (0-9), binary arithmetic operates on a base-2 system using only 0 and 1. This tool simulates the behavior of a hardware Full Adder, breaking down the calculation bit by bit. Accuracy in binary summation is critical for low-level programming, network subnetting, and understanding machine architecture logic.
The primary challenge in learning binary arithmetic is managing the "carry" bit. In decimal, 9 + 1 forces a carry to the next column. In binary, this threshold is much lower: 1 + 1 results in 0 with a carry of 1 (yielding 102, which is 2 in decimal). This calculator visualizes this propagation, ensuring students grasp the mechanics of the Arithmetic Logic Unit (ALU).
Formulas
The logic behind binary addition relies on boolean algebra, specifically the XOR and AND operations found in digital circuits. A single column addition is defined by:
Sum = A &xor; B &xor; Cin
Cout = (A ∧ B) ∨ (Cin ∧ (A &xor; B))
Where Cin is the carry from the previous position and Cout is the carry passed to the next significant bit.
Reference Data
| Input A | Input B | Carry In (Cin) | Sum Result (S) | Carry Out (Cout) | Decimal Value |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 | 2 |
| 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 2 |
| 0 | 1 | 1 | 0 | 1 | 2 |
| 1 | 1 | 1 | 1 | 1 | 3 |