C OMBINATIONAL L OGIC D ESIGN 1 Eng.Maha AlGubali

C OMPUTER C OMPONENTS Computer components are made from both:  combinational.  sequential logic circuits. First we will look at Combinational Logic Circuit 2 Eng.Maha AlGubali

C OMBINATIONAL C IRCUITS Combinational Circuits – Consist of logic gates whose outputs at any time are determined from the present combination of inputs. input variables, logic gates, and output variables – The logic gates accept signals from the inputs and generate signals to the output 3 Eng.Maha AlGubali

D ESIGN P ROCEDURE Similar to software 1. Specification – problem description Write a specification for the circuit 2. Formulation – as truth table, Boolean function, or ( Verilog ) define the required relationships between inputs and outputs 3. Optimization – used to be manual, now CAD tool Draw a logic diagram or provide a netlist for the resulting circuit (AND, OR, INVERTORS) 4. Mapping – to the implementation technology Transform the diagram to a new diagram using the available implementation technology 5. Verification – used to be manual, now simulation Verify correctness of design 4 Eng.Maha AlGubali

E XAMPLE 1 Specification: 3 binary inputs; Output is 1 when input < Formulation Optimization Eng.Maha AlGubali

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1 BIT HALF ADDER Bit Addition Unit (Half Adder) The truth table summaries the outputs of the 1 bit addition based on values of x and y The two outputs are sum and carry As we see, the sum can be found using the “XOR” operation and the carry using the “AND” operation This circuit is known as half adder Does half the job – does not account for carry-in input 7 Eng.Maha AlGubali

1 B IT A DDITION U NIT (F ULL A DDER ) 8  The full adder becomes necessary when a carry input must be added to the two binary digits to obtain the correct sum. A half adder has no input for carries from previous circuits. Eng.Maha AlGubali

MULTIPLEXER A combinational circuit that selects binary information from one of many input lines and directs it to a single output line – Normally, there are 2n input lines and n selection lines whose bit combinations determine which input is selected – also called a data selector 9 Eng.Maha AlGubali. 2 n input line. …. n Selected line output

MULTIPLEXER ( CONT ) The truth table for a 2-to-1 multiplexer is:. 10 Eng.Maha AlGubali

DECODERS A combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines. n-to-m-line decoders: generate m (=2 n or fewer) minters of n input variables 11 Eng.Maha AlGubali n-to-m Line Decoder. n input line. m output line

3 TO 8 LINE DECODER 12 Eng.Maha AlGubali 3-to-8 Line Decoder Block diagram Logic diagram

ENCODER An encoder has 2 n (or fewer) input lines and n output lines, which generate the binary code corresponding to the input value. 13 Eng.Maha AlGubali 2 n -to-n Line Decoder. 2 n input line. n output line