Lecture 4: Karnaugh Maps, Timing Diagrams ... - CS-CSIF

3.1. Multiplexers are used to control signal and data routing.3.2. We can use a n-input MUX to implement any Boolean equation of log 2 (n) variables by feeding the variables to theselect inputs, and setting the data inputs to the expected values for the equation.3.2.1. For the following 4-to1 MUX, what are the constant voltages (high = true, low = false) applied to the four Datainputs to implement XOR based the select inputs?4. Decoders s are combinational circuits that convert binary information from n input lines to a maximum of 2 n uniqueoutput lines.4.1. For many designs, only one output is asserted at a time, which is called one-hot encoded. This type is extremelyimportant in memory circuits, since you give an address that is encoded and one of the spots in the memory hasto be selected. Most kinds of random-access memory use a n-to-2 n decoder to convert the selected address on theaddress bus to one of the row address select lines.4.2. An additional input that is attached to all of the AND gates can be used in two ways.4.2.1. If data is fed to that input, then the decoder can be used a s demultiplexer that guides the data to a specificoutput, i.e. a 2 n -to-1 demultiplexer.4.2.2. If the additional input line is thought of as a separate enabling input, then it is a way to turn the decoder on oroff.5. Adder = a digital circuit that adds two numbers.5.1. Half adder adds two single binary digits A and B. It has two outputs, sum (S) and carry (C).5.2. Full adder adds binary numbers and accounts for values carried in as well as out. Notice that the longest path (A to C out )goes through three gates. This will be involved in determining the clock speed.