Logic Gates

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Using Boolean logic's AND, OR, and NOT gates, the basis of all physical computing is formed. We played with their concept on Monday, Week 2.

AND			OR			NOT
Inputs		Output	Inputs		Output	Input	Output
0	0	0	0	0	0	0	1
1	0	0	1	0	1	1	0
0	1	0	0	1	1
1	1	1	1	1	1

From these three, derivatives such as NAND (made with an AND gate's output into a NOT), NOR (OR outputting into NOT) and XOR (a combination of two AND gates, an OR gate, and a NOT gate such that the normal AND positive becomes a negative for the OR) can be made. Each gate also has its own symbol.

The OR Gate			The AND Gate
The NOT Gate			The XOR Gate
The NOR Gate			The NAND Gate

I made two different adders using only these six gates;

This adder can add two inputs of one or zero together.

This adder can add three inputs of one or zero together.

The strategy I found myself using was to evaluate for each scenario and output level, not just all of the outputs at once. For example, in the 3-input adder, I not only had to make a specific circuit for when all three are ones and how to get the correct output diode states, but I also evaluated five other scenarios; one for when one of the top two inputs and the bottom input were both on, one for when one of the bottom two inputs and the top input were both on, one for when only one of the bottom two inputs was the only one on, one for when only two of the top two inputs was the only one on, and a last one for all inputs in an off state.

We continued this on Wednesday, Week 2.

Stacking onto the previous adders, now termed "half-adders" and "full adders" respectively (the half adder can add two inputs, while three inputs can account for carrying over higher numbers for a full adder and huge potential), we went over the most efficient full adder and how to stack them to make multi-bit calculators.

This adder has 8 units which can count up to 9 bits, or individual binary units in a number.