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Half Adder & Full Adder Explained — How Computers Add Numbers
How does a computer add two numbers — not with code, but with actual electronics? In this video we build the circuits that make addition happen at the hardware level, starting from the simplest possible adding circuit and working up to something that can add multi-bit binary numbers.
We cover:
• The rules of binary addition (and why carrying works the same as primary school)
• The half adder — the smallest adding circuit, built from one XOR gate and one AND gate
• The full adder — why the half adder isn't enough, and how to fix it with two half adders and an OR gate
• The ripple carry adder — chaining full adders together to add 4-bit (and larger) binary numbers
• Overflow — what happens when the answer doesn't fit
Everything is demonstrated in a logic gate simulator so you can see exactly how the signals flow through the circuit. No code required — just logic gates doing what they do.This is the foundation of how virtually every processor ever built handles addition. Next time we'll look at how computers deal with fractions and floating-point numbers — which is where things get weird.
-- Chapters --
0:00 Introduction — How do computers add?
0:53 Binary addition rules
2:41 The half adder (XOR + AND gates)
5:28 Half adder demo in the simulator
7:15 Why the half adder isn't enough
8:20 The full adder (two half adders + OR gate)
10:45 Full adder demo in the simulator
12:30 The ripple carry adder
14:15 4-bit adder demo & overflow
15:40 Conclusion & what's next
“Music by Karl Casey @ White Bat Audio”
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By How does a computer add two numbers — not with code, but with actual electronics? In this video we build the circuits that make addition happen at the hardware level, starting from the simplest possible adding circuit and working up to something that can add multi-bit binary numbers.
We cover:
• The rules of binary addition (and why carrying works the same as primary school)
• The half adder — the smallest adding circuit, built from one XOR gate and one AND gate
• The full adder — why the half adder isn't enough, and how to fix it with two half adders and an OR gate
• The ripple carry adder — chaining full adders together to add 4-bit (and larger) binary numbers
• Overflow — what happens when the answer doesn't fit
Everything is demonstrated in a logic gate simulator so you can see exactly how the signals flow through the circuit. No code required — just logic gates doing what they do.This is the foundation of how virtually every processor ever built handles addition. Next time we'll look at how computers deal with fractions and floating-point numbers — which is where things get weird.
-- Chapters --
0:00 Introduction — How do computers add?
0:53 Binary addition rules
2:41 The half adder (XOR + AND gates)
5:28 Half adder demo in the simulator
7:15 Why the half adder isn't enough
8:20 The full adder (two half adders + OR gate)
10:45 Full adder demo in the simulator
12:30 The ripple carry adder
14:15 4-bit adder demo & overflow
15:40 Conclusion & what's next
“Music by Karl Casey @ White Bat Audio”