Lect9 Combinational Circuits
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Transcript of Lect9 Combinational Circuits
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7/29/2019 Lect9 Combinational Circuits
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TA C162
Lecture 9 Combinational Circuits
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Todays AgendaDemorgans Law
Adder
Full Adder
Saturday, January 30, 2010 2Biju K Raveendran@BITS Pilani.
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Demorgans Law Suppose we complement an input before
.
For example, consider
Observe, if inputs are 0 and 1
then out ut is 1.
Saturday, January 30, 2010 3Biju K Raveendran@BITS Pilani.
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Demorgans Law -Converting AND to OR
Exercise:
A B A B A.B (A.B)
0 1 1 0 0 1
1 1 0 0 0 1
Saturday, January 30, 2010 4Biju K Raveendran@BITS Pilani.
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Demorgans Law
(A.B) = A+B
(A+B) = A.B
. represents Logic AND
+ represents Logic OR represents Logic NOT
Saturday, January 30, 2010 5Biju K Raveendran@BITS Pilani.
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DeMorgan's LawFirst Law
. . . . . = = + + + + .
Second Law
A+B+C+D . = = A.B.C.D. .
Here . represents Logic AND
+
Saturday, January 30, 2010 6Biju K Raveendran@BITS Pilani.
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Logic Structures 2 kinds Storage Structures
Permits the storage of information (as bits)
ec s on ruc ures
Does not include storage of information
Outputs strictly depend on the combination of thecurrent in ut values
Outputs are not dependent on the past historystored internally (no information can be storedn erna y n a com na ona ogc c rcu
Saturday, January 30, 2010 7Biju K Raveendran@BITS Pilani.
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Combinational Logic Structures
Full Adder
Multiplexer (MUX)
Saturday, January 30, 2010 8Biju K Raveendran@BITS Pilani.
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Lets Design a Circuit for Binary Addition
Requirement
Adds the 2 bits given and produces sum and carry
(Half) ADDER
0 0 1 1
0 1 0 1
sum
carr
Before proceeding to attempt drawing circuit Understand the input/output of the circuit
Define the behavior of the circuit using truth table
Write the Sum of Products SOP Boolean ex ressions from the
truth table We dont bother the simplification process involved in reducing
the circuitry complexity for now.
Saturday, January 30, 2010 9Biju K Raveendran@BITS Pilani.
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Adding two bits: Half AdderTruth Table:A B Sum Carry
0 0 0 00 1 1 0
1 0 1 0
Boolean Expressions
C = A AND B
10
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Adding Three Bits: Full Adder4-Bit Full Adder
Requirement: Adds the two bits and a carry
Saturday, January 30, 2010 11Biju K Raveendran@BITS Pilani.
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Full Adder Performs the addition in column i
3 inputs: ai, bi and ci
ai i c i+1 s i0 0 0 0
2 outputs: si and ci+1 ci is the carry in from bit position i-1
1 0 0 11 1 1 0
ci+1 is the carry out to bit position i+1
a a ... a a
n 1 n 2 1 0b b ... b b +
n 1 n 2 1c c ... c +
n n ...
Saturday, January 30, 2010 12Biju K Raveendran@BITS Pilani.
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Full Adder: Truth TableA B Cin S Cout0 0 0 0 0
0 1 0 1 0
1 0 0 1 0
1 1 0 0 1
SOP for Sum S = A.B.C + A.B.C + A.B.C + A.B.C
= . . . . . . . .
Saturday, January 30, 2010 13Biju K Raveendran@BITS Pilani.
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Full Adder Logic Implementation
Saturday, January 30, 2010 14Biju K Raveendran@BITS Pilani.