Question

I am trying to make a circuit using only NAND gates that would represent the result of a vote by people. So there would be 11 inputs and the result is shown by an LED. Since it's 11 people, if the majority of people say yes (1) than the result will be yes (led on). What would the k-map, equation, and circuit using NAND gates look like?

Answer 1

Bro thanks for being patience. only one way we can do to make it small. Each Full Adder consists of 2 xor gates, 2 and gates, 1 or gate( All gates are 2 inputs). I have used 18 Full Adders for count from 0 to 16. It can take upto 16 inputs, which means 16 votes can be implement. you take 11 inputs and ground other 5 inputs so that you can get 11 people votes. Total 2 input gates - 36 xor,36 and 18 or gates. To make LED work ,1 And gate & 1 or gate.

Total 92 gates required. If you want to use nand gates only it will be more , but possible.

If you want exactly 11 votes use only 11 inputs the other 5 inputs are grounded.

And in 11 votes, greater than 5 is majority votes which means 6 - 11.

If you want to use 16 inputs, majority will be 9 - 16 votes, so you can change output logic between Count_1s circuit and LED .

This is Snapshot for adder circuit. That circuit is simulated in multisim and in working condition. you can go ahead with breadboard.

1) Black Box for count number of 1's

2)Gray Box for Count number of 1's.

3) FULL ADDER Circuit

4) Completion of full circuit

test 5 votes input

test_6 input votes 6

Majority means greater than 5.

You need Adder cicuit followed by comparator.

comparator compares whether the result is greater than 5 or not

then it will give output as 1 if greater than 6 else 0.

For k-map , you have to use 11 inputs. which is combinations of 2^11 = 2048 combinations will come.

This is very complex logic that you never go for k-maps and equations for problems like this.

you can get as simple as this if you use verilog program. and then convert to nand logic. which most eda tools will do.

//Verilog Code

module vote(
input [10:0] people,
output reg LED

);

reg [3:0]value;
always@(*) //adder circuit
value = people [10] + people [9] + people[8] + people [7] +
people [6] + people [5] + people[4] + people [3] +
       people [2] + people [1] + people[0];

always@(*) begin //comparator circuit
if( value > 5)
LED = 1'b1; //LED will glow
else
LED = 1'b0; //LED off.
end
endmodule

still you want that kmap and kinda logic equation, just google it how big it will come.