About

Understanding binary addition is often easier when visualized vertically, similar to how we learn decimal addition in school. This tool slows down the process, animating the calculation from the Least Significant Bit (LSB) to the Most Significant Bit (MSB). It explicitly highlights the "carry chain"-the ripple effect that occurs when bits sum to 2 (binary 10) or 3 (binary 11).

This visualization is crucial for students of Computer Architecture, as it mimics the clock cycles of a serial adder or the propagation delay in a ripple-carry adder. By observing the carry bit move column by column, users gain an intuitive feel for why binary arithmetic behaves the way it does.

Formulas

The core rules for a single column of binary addition are:

0 + 0 = 0

1 + 0 = 1

1 + 1 = 0 (Carry 1)

1 + 1 + 1 = 1 (Carry 1)

Reference Data

Expression	Sum Bit (Result)	Carry Bit (Next Col)	Decimal Equiv
0 + 0	0	0	0
1 + 0	1	0	1
0 + 1	1	0	1
1 + 1	0	1	2
1 + 1 + 1	1	1	3

Frequently Asked Questions

Just like in decimal addition, a value that exceeds the limit of a single digit (1 in binary, 9 in decimal) must be moved to the next higher place value (the column to the left) to maintain mathematical correctness.

The Play button starts an animation that highlights each column one by one, showing exactly how the computer calculates the sum and moves the carry. It is a slow-motion replay of the addition.

This visualization assumes Unsigned Integers. While the bitwise mechanics are identical for Two's Complement (signed) addition, the interpretation of the final result (overflow vs. negative) differs.