How to Build Logic Gates with More Red
Basic Gates
Place an AND Gate, OR Gate, NOT Gate, NAND Gate, or NOR Gate and feed redstone into its inputs. Each gate has a fixed input side and output side; use the Pliers to rotate a placed gate if it faces the wrong way.
Bitwise Gates
For multi-bit work, use the Bitwise family: Bitwise AND Gate, Bitwise OR Gate, Bitwise XOR Gate, Bitwise XNOR Gate, Bitwise NOT Gate, Bitwise Diode, and Bitwise Multiplexer. These operate on a whole signal value rather than a single on/off state, so they are what you use when a circuit needs to compare or combine numbers.
Combining Gates
Feed the output of one gate into the input of the next. A common pattern is two inputs into an AND Gate, then that output into a NOT Gate to get a NAND result. Use a Latch after the final gate to hold the result.
Use a Multiplexer when you need to choose between two inputs based on a third. Use a Pulse Gate when a gate's output must be a single short pulse rather than a held signal.
Check any gate's current output with the Hexidecrubrometer. If a gate is not responding, verify that its inputs are actually receiving signal and that its output side is not blocked.