This one was a lot of fun, IMO.

    enum Command
    {
        NONE,
        LSHIFT,
        RSHIFT,
        NOT,
        AND,
        OR
    }

    static ushort ResolveConnections(string wire, Dictionary<string, string> inputs, Dictionary<string, ushort> wires)
    {
        ushort result = 0;
        string[] instruction;

        if (inputs[wire].Contains(" "))
            instruction = inputs[wire].Split(' ');
        else
            instruction = new string[] { inputs[wire] };

        Command command = Command.NONE;

        foreach (var p in instruction)
        {
            switch (p)
            {
                case "LSHIFT": command = Command.LSHIFT; break;
                case "RSHIFT": command = Command.RSHIFT; break;
                case "NOT": command = Command.NOT; break;
                case "AND": command = Command.AND; break;
                case "OR": command = Command.OR; break;
                default:
                    switch(command)
                    {
                        case Command.NONE:
                            ushort temp;
                            if (ushort.TryParse(p, out temp))
                                result = ushort.Parse(p);
                            else
                            {
                                if (!wires.ContainsKey(p))
                                    wires[p] = ResolveConnections(p, inputs, wires);
                                result = wires[p];
                            }
                            break;
                        case Command.LSHIFT:
                            result <<= int.Parse(p);
                            break;
                        case Command.RSHIFT:
                            result >>= int.Parse(p);
                            break;
                        case Command.NOT:
                            result = (ushort)~ResolveConnections(p, inputs, wires);
                            break;
                        case Command.AND:
                            result &= ResolveConnections(p, inputs, wires);
                            break;
                        case Command.OR:
                            result |= ResolveConnections(p, inputs, wires);
                            break;
                        default:
                            Console.WriteLine("What now?");
                            break;
                    }
                    command = Command.NONE;
                    break;
            }

        }

        return result;
    }

    public static ushort Part1()
    {
        System.IO.StreamReader file = new System.IO.StreamReader(@"day7_input.txt");
        string line;

        Dictionary<string, ushort> wires = new Dictionary<string, ushort>();
        Dictionary<string, string> inputs = new Dictionary<string, string>();

        while ((line = file.ReadLine()) != null)
        {
            string[] temp = line.Split(new string[] { " -> " }, StringSplitOptions.None);

            inputs[temp[1]] = temp[0];
        }

        ushort value = ResolveConnections("a", inputs, wires);
        Console.WriteLine("d5p1: The value of a is: " + value);

        return value;
    }

    public static void Part2()
    {
        System.IO.StreamReader file = new System.IO.StreamReader(@"day7_input.txt");
        string line;

        Dictionary<string, ushort> wires = new Dictionary<string, ushort>();
        Dictionary<string, string> inputs = new Dictionary<string, string>();

        while ((line = file.ReadLine()) != null)
        {
            string[] temp = line.Split(new string[] { " -> " }, StringSplitOptions.None);

            inputs[temp[1]] = temp[0];
        }

        wires["b"] = Part1();

        Console.WriteLine("d5p2: The value of a is: " + ResolveConnections("a", inputs, wires));
    }