Implementing Logic Gates in a Spreadsheet

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 string 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