I have one input which its states can be 1 or z (high impedance) and the result should be 1 and 0 respectively. Can anyone design a logical function for this? thanks.
Edited Part:
As you can see the output of the highlighted OR can be z or 1, I want to make 0 from z and 1 out of 1. how?
This can be easily accomplished with a pulldown resistor. That's a fancy name for a resistor to ground. The resistor value is set low enough so that the line is held solidly in the logic low state when nothing else is driving it. The value is high enough to not exceed the current source capability of anything that needs to drive the line high.
For example, let's say the line can be driven by a CMOS logic output that can source up to 4 mA in the high state. At 3.3 V, it takes (3.3 V)/(4 mA) = 825 Ω to draw 4 mA. That's the lowest allowed pulldown resistance. You could safely use 1 kΩ, for example.
There are more tradeoffs, so see this explanation of pullup resistors. Pullups are the same concept, except the line is held high when not driven instead of low.
You are asking about a line that is either left high-z or actively driven high. However, that is very unlikely what is actually happening here. You show this line being driven by a OR gate. Those usually either drive actively in both directions, or sometimes drive actively low with high-z for the other state. Check the datasheet.
Asking for a "truth table" for this makes no sense.
These two confusions indicate that you have too many basic misconceptions and too little basic knowledge for a reasonable answer here to be possible. The best I can suggest is to give this project to someone that knows what they are doing. Perhaps you can learn a little from them.
Your circuit looks a bit like a microcontroller connected to a keypad and the 4 or gates allow generating an interrupt if someone presses any key. Your OR gates outputs will likely only output 0 or 1 but never Z. You should be concerned about the inputs of the 2 OR gates on the left. To check if a key is pressed, you would drive that row input (A-D) to 1 and the other row inputs to Z. You configure the microcontroller pins as pull-down and read their status, if it 1 then the key is pressed, if it is 0 then the key is not pressed.
If you want to generate an interrupt, if any key is pressed you would drive A to D with 1 and configure the pins 1-4 as pulldown. As long as no key is pressed the output of your OR gate will be 0 and if any key is pressed the output of the OR gate would be 1 and if the MCU pin connected to the OR gate is a interrupt pin, you could use that to wake up from sleep. If it is not a interrupt pin the OR gates are not really needed and everything they do can easily be achieved using only software.
