half adder

Previously, we saw how addition consists of two parts:

• Adding digits together
• Handling the carry

We’re going to forget about the carry for now, and just build a device that can add digits.

adding binary digits

We already know we can add two binary digits together, just like with base ten:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0 (carry 1)

If we ignore the carry, this looks like the truth table . That’s an XOR gate! In other words, an XOR gate performs a physical representation of adding binary digits together.

In this demo, the XOR gate is literally adding together the digits of these two streams (ignoring the carry). We can say our XOR gate is functioning as a half adder.

Next we’ll look at handling the carry so we can turn this into a full adder.

continue