Here are some of the basic logic gates, implemented as spreadsheet formulas.
| Gate | Spreadsheet Formula |
|---|
| AND | AND(A,B) |
| OR | OR(A,B) |
| NOT | NOT(B) |
| NAND | NOT(AND(A,B)) |
| NOR | NOT(OR(A,B)) |
| XOR | OR(AND(A,NOT(B)),AND(NOT(A),B)) |
| XNOR | NOT(OR(NOT(OR(A,NOT(OR(A,B)))),NOT(OR(B,NOT(OR(A,B)))))) |
It is possible to implement any gate using only NOT and OR (NOR), or with NOT and AND (NAND) gates. For example, here is an AND gate implemented using only NOT and OR gates:
| AND using only NOR gates | NOT(OR(NOT(OR(A,A)),NOT(OR(B,B))) |
With AND, OR and NOT, we can implement a half adder, like this:
| Column A | Column B |
|---|
| A | 0 |
| B | 1 |
| Carry (AND) | =AND(B1,B2) |
| Sum (XOR) | =OR(AND(B1,NOT(B2)),AND(NOT(B1),B2)) |
By stringing together two half adders and OR-ing the carry bit, we can create a full adder:
| Bit | Spreadsheet Formula |
|---|
| A | 0 |
| B | 0 |
| Cin | 0 |
| Cout | =AND(B2,B3) |
| Sum | =OR(AND(B2,NOT(B3)),AND(NOT(B2),B3)) |
| Cout | =AND(B6,B4) |
| Sum | =OR(AND(B4,NOT(B6)),AND(NOT(B4),B6)) |
| Cout | =OR(B7,B5) |
| Sum | =B8 |
Implementing a 4-bit adder is just a matter of simply replicating the full adder logic four times:
| 8 | 4 | 2 | 1 |
|---|
| Input A | 0 | 0 | 0 | 0 |
| Input B | 0 | 0 | 0 | 0 |
| A | =B2 | =C2 | =D2 | =E2 |
| B | =B3 | =C3 | =D3 | =E3 |
| Cin | =C12 | =D12 | =E12 | 0 |
| Cout | =AND(B5,B6) | =AND(C5,C6) | =AND(D5,D6) | =AND(E5,E6) |
| Sum | =OR(AND(B5,NOT(B6)),AND(NOT(B5),B6)) | =OR(AND(C5,NOT(C6)),AND(NOT(C5),C6)) | =OR(AND(D5,NOT(D6)),AND(NOT(D5),D6)) | =OR(AND(E5,NOT(E6)),AND(NOT(E5),E6)) |
| Cout | =AND(B7,B9) | =AND(C7,C9) | =AND(D7,D9) | =AND(E7,E9) |
| Sum | =OR(AND(B7,NOT(B9)),AND(NOT(B7),B9)) | =OR(AND(C7,NOT(C9)),AND(NOT(C7),C9)) | =OR(AND(D7,NOT(D9)),AND(NOT(D7),D9)) | =OR(AND(E7,NOT(E9)),AND(NOT(E7),E9)) |
| Cout | =OR(B8,B10) | =OR(C8,C10) | =OR(D8,D10) | =OR(E8,E10) |
| Sum | =B11 | =C11 | =D11 | =E11 |
