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← CPUs Lesson 3 / 6

The Binary Adder

Adding in binary is just one rule — 1+1 = 0 carry 1 — exactly like carrying the 1 in school. Resolve one column at a time and watch the carry ripple left.

Flip the bits

A
= 6
B
= 5

0 of 4 columns resolved, from the right (the LSB). Toggling any bit starts over.

Ripple-carry adder

col 3
0 + 0
c-in · ? c-out ·
col 2
1 + 1
c-in · ? c-out ·
col 1
1 + 0
c-in · ? c-out ·
col 0
0 + 1
c-in · ? c-out ·

Result

? ? ? ? ?

Press Step to resolve the next column. Each one passes its carry to the column on its left.

Math isn't built into the chip — it's wired up from XOR (the sum) and AND (the carry) gates, and that carry is exactly why addition ripples.