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The basic adding circuit is just that, basic! It consists of a XOR gate and an AND gate to give you the basic output with a carry bit.

The XOR gate is short for exclusive or. In a regular OR gate, 0 and 0 equal 0, 1 and 0 equal 1, 1 and 1 equal 1. In an exclusive or gate, 0 and 0 equal 0, 1 and 0 equal 1, 1 and 1 equal 0. This is important because when adding 1 and 1 in binary you get 10, so the ones place has a zero, something that can't be done with a basic OR gate.

OR:

A B Y

0 0 0

1 0 1

0 1 1

1 1 1

XOR:

A B Y

0 0 0

1 0 1

0 1 1

1 1 0

So now, when you add 1 and 0, you get 1, but hold on...When you add 1 and 1, you get 0?? That can't be right! In order to fix that, we need to be able to have 1 and 1 equal 10. Welcome to the AND gate. As the name implies, an AND gate equals 1 when A=1 AND B=1. This it tied in parallel with the XOR gate and is the carryout bit, so that when you add 1+1, you CAN get 10!

The XOR gate is short for exclusive or. In a regular OR gate, 0 and 0 equal 0, 1 and 0 equal 1, 1 and 1 equal 1. In an exclusive or gate, 0 and 0 equal 0, 1 and 0 equal 1, 1 and 1 equal 0. This is important because when adding 1 and 1 in binary you get 10, so the ones place has a zero, something that can't be done with a basic OR gate.

OR:

A B Y

0 0 0

1 0 1

0 1 1

1 1 1

XOR:

A B Y

0 0 0

1 0 1

0 1 1

1 1 0

So now, when you add 1 and 0, you get 1, but hold on...When you add 1 and 1, you get 0?? That can't be right! In order to fix that, we need to be able to have 1 and 1 equal 10. Welcome to the AND gate. As the name implies, an AND gate equals 1 when A=1 AND B=1. This it tied in parallel with the XOR gate and is the carryout bit, so that when you add 1+1, you CAN get 10!

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