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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 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.

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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.

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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.

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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

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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

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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

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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’

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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

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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)

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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

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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

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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

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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:

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

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