So what’s a multiplexer you ask? A multiplexer is an integrated circuit that takes a number of inputs and outputs a smaller number of outputs. In this case we’re aiming at creating a 4-to-1 multiplexer. As the name implies, it takes four inputs and outputs exactly one output, determined by a select input. Depending on the number of input lines, one or more select lines may be required. For 2n input lines, n select lines are needed. In hardware terms, this is basically the simplest of switches.
Most people can do simple decimal addition in their heads, and even advanced addition using common rules like carrying. Here’s how we’d add 6 + 7: