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Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzyCombinational CircuitsCombinational Circuits
Dr. Ahmed El-BialyDr. Ahmed El-Bialy
Dr. Sahar FawzyDr. Sahar Fawzy
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
Combinational CircuitsCombinational Circuits
A combinational circuit consists of logic A combinational circuit consists of logic gates whose outputs at any time are gates whose outputs at any time are determined by the inputs using logic determined by the inputs using logic operations.operations.
For n input variables, there are 2n possible binary input combinations.
For each binary combination of the input variables, there is one possible binary value on each output.
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
Combinational CircuitsCombinational 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-B
ialy,
Dr. Sahar F
awzy
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-B
ialy,
Dr. Sahar F
awzy
Combinational Circuit Analysis
T1 = B’C T2 = A’B
T3 = A+T1=A+B’C
T4 = T2 D =(A’B) D = A’BD’ + AD + B’D
T5 = T2 +D = A’B + D
F1 = T3 + T4 = A + B’C +A’BD’+AD+B’D
=A +B’C + BD’ + B’D
F2 = T5 = A’B + D
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
Combination Circuit DesignCombination 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-B
ialy,
Dr. Sahar F
awzy
Code Converter ExampleCode 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-B
ialy,
Dr. Sahar F
awzy
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
ABCD
00 11 1001
00
11
10
01
1
0 1
0 0
1 1 0
0 1 1
1 1
0 0
0
a = A’C + A’BD + A’B’D’+
AB’C’AC
BD
C’
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
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-B
ialy,
Dr. Sahar F
awzy
Signed Binary Addition and Signed Binary Addition and SubtractionSubtraction
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, C0=1 and it performs A-B (A adds the 2’s complement of B)
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
DecoderDecoderA decoder is a combinational circuit that converts binary information from the n coded inputs to a maximum of 2n unique outputs
• Three inputs A0-A3
are decoded into eight outputs D0-D7
• Each output Di represents one of minterms of the 3 inputs.
• The output variables are mutually exclusive
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
Decoder: Decoders are a handy source of minterms. Any
combinational circuit with n inputs and m outputs can be implemented with a n-to-2n-line decoder and m OR gates
Recall full adder equations, and let AiBiCi be the minterm index: Si(Ai, Bi, Ci)= m ( 1, 2, 4, 7 ) and
Ci+1(Ai, Bi, Ci) = m ( 3, 5, 6, 7 )
Since there are 3 inputs and a total of 8 minterms, we need a 3-to-8 decoder
Si
Ci+1
Ai
Bi
Ci
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzy
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-B
ialy,
Dr. Sahar F
awzy
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 2n-to-1 multiplexer, there are 2n input lines and n selection lines whose bit combination determines which input is selected.
4-to-1 MUX:
Dr. Ahmed El-B
ialy,
Dr. Sahar F
awzyThank youThank you
see you in see you in Sequential CircuitsSequential Circuits