 # Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Combinational Circuits Dr. Ahmed El-Bialy Dr. Sahar Fawzy.

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Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Combinational Circuits Dr. Ahmed El-Bialy Dr. Sahar Fawzy

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Combinational Circuits A combinational circuit consists of logic gates whose outputs at any time are determined by the inputs using logic operations. A combinational circuit consists of logic gates whose outputs at any time are determined by the inputs using logic operations.   For n input variables, there are 2 n possible binary input combinations.   For each binary combination of the input variables, there is one possible binary value on each output.

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Combinational Circuits A combinational circuit can be described by: A truth table that lists the output values for each combination of the input variables, OR m Boolean functions, one for each output variable.

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy  Analysis of a combinational circuit is the determination of the Boolean function that the circuit implements. Combinational Circuit Analysis  The analysis starts with a given logic circuit diagram and ends with a set of Boolean functions OR a truth table  Proceed from inputs to outputs (systematically).  Label intermediate functions.  Simplify as possible.

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Combinational Circuit Analysis T 1 = B’C T 2 = A’B T 3 = A+T 1 =A+B’C T 4 = T 2  D =(A’B)  D = A’BD’ + AD + B’D T 5 = T 2 +D = A’B + D F 1 = T 3 + T 4 = A + B’C +A’BD’+AD+B’D =A +B’C + BD’ + B’D F 2 = T 5 = A’B + D

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Combination Circuit Design  Design of a combinational circuit is the development of a circuit from a description of its function  Procedure: - Problem statement - Truth table and describing Boolean Algebra - Simplification - Implementation - Verification

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Code Converter Example Design a circuit that converts a binary-coded-decimal (BCD) to the seven signals required to drive a seven- segment light-emitting diode (LED) display. Assuming the signal 1 illuminates the segment and a logic-0 signal turns off the segment

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Code Converter Example  Derive the Boolean function for each output - e.g., using the following K-map to derive the Boolean function for output a AB CD 001110 01 00 11 10 01 1 01 00 110 011 11 00 0 a = A’C + A’BD + A’B’D’+ AB’C’ A C B D C’

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Adder Design Example  By cascading four 1-bit full adders so that the carry out from one becomes the carry in to the next higher bit position, we can construct a 4-bit adder

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Signed Binary Addition and Subtraction  Representing negative numbers in their 2’s complement representation, the addition and subtraction of two signed numbers are the same as that of two unsigned numbers.  4-bit Adder-subtractor circuit: when s=0, it performs A+B; when s=1, C 0 =1 and it performs A-B (A adds the 2’s complement of B)

Dr. Ahmed El-Bialy, Dr. Sahar FawzyDecoder  A decoder is a combinational circuit that converts binary information from the n coded inputs to a maximum of 2 n unique outputs Three inputs A 0 -A 3 are decoded into eight outputs D 0 -D 7 Each output D i represents one of minterms of the 3 inputs. The output variables are mutually exclusive

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Decoder:  Decoders are a handy source of minterms. Any combinational circuit with n inputs and m outputs can be implemented with a n-to-2 n -line decoder and m OR gates  Recall full adder equations, and let A i B i C i be the minterm index: S i (A i, B i, C i )=  m ( 1, 2, 4, 7 ) and C i+1 (A i, B i, C i ) =  m ( 3, 5, 6, 7 )  Since there are 3 inputs and a total of 8 minterms, we need a 3-to-8 decoder SiSi C i+1 AiAi BiBi CiCi

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Decoder:  Large decoder construction: Example: a 3-to-8 decoder can be built from two 2- to-4 decoders with the use of enable Enable =0 forces all outputs to 0

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Multiplexer  A digital multiplexer is a combinational circuit that selects one input from many input lines and directs it to a single output line.  For a 2 n -to-1 multiplexer, there are 2 n input lines and n selection lines whose bit combination determines which input is selected.  4-to-1 MUX:

Dr. Ahmed El-Bialy, Dr. Sahar Fawzy Thank you see you in Sequential Circuits

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