Chapter 3Boolean Algebra and Digital Logic2 Combinational CircuitsA combinational circuit consists of logic gates whose outputs, at any time, are determined by combining the values of the inputs.For n input variables, there are 2n possible binary input combinations.For each binary combination of the input variables, there is one possible output.3.4 Digital ComponentsThe main thing to remember is that combinations of gates implement Boolean functions.The circuit below implements the Boolean function:3We simplify our Boolean expressions so that we can create simpler circuits.3.5 Combinational CircuitsWe have designed a circuit that implements the Boolean function:This circuit is an example of a combinational logic circuit.Combinational logic circuits produce a specified output almost! at the instant when input values are applied.In a later section, we will explore circuits where this is not the case.43.5 Combinational CircuitsCombinational logic circuits give us man" useful devices.#ne of the simplest is the half adder$ which finds the sum of two bits.We can gain some insight as to the construction of a half adder b" loo%ing at its truth table$ shown at the right.53.5 Combinational CircuitsAs we see$ the sum can be found using the ' operation and the carr" using the A(D operation.63.5 Combinational CircuitsWe can change our half adder into to a full adder b" including gates for processing the carr" bit.The truth table for a full adder is shown at the right.73.5 Combinational Circuits)ow can we change the half adder shown below to ma%e it a full adder*83.5 Coambinational Circuits)ere+s our completed full adder.93.5 Combinational Circuits,ust as we combined half adders to ma%e a full adder$ full adders can connected in series.The carr" bit -ripples. from one adder to the next/ hence$ this configuration is called a ripple-carry adder.10Todays systems employ more efficient adders. 3.5 Combinational CircuitsDecoders are another important t"pe of combinational circuit.Among other things$ the" are useful in selecting a memor" location according a binar" value placed on the address lines of a memor" bus.Address decoders with n inputs can select an" of 0n locations. 11This is a block diagram for a decoder. 3.5 Combinational CircuitsThis is what a 01to12 decoder loo%s li%e on the inside.12If x = 0 and y = ! which output line is enabled" 3.5 Combinational CircuitsA multiplexer does 3ust the opposite of a decoder.4t selects a single output from several inputs.The particular input chosen for output is determined b" the value of the multiplexer+s control lines.To be able to select among n inputs$ log0n control lines are needed. 13This is a block diagram for a multiplexer. 3.5 Combinational CircuitsThis is what a 21to15 multiplexer loo%s li%e on the inside.14If #0 =and #

= 0! which input is transferred to the output" 3.5 Combinational CircuitsThis shifter moves the bits of a nibble one position to the left or right.15If # = 0! in which direction do the input bits shift"