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LOGIC CIRCUIT

LOGIC CIRCUIT. Part 2: DESIGN CIRCUIT. LOGIC CIRCUIT DESIGN. x y z F 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1. Truth Table. Boolean Function.

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LOGIC CIRCUIT

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  1. LOGIC CIRCUIT Part 2: DESIGN CIRCUIT

  2. LOGIC CIRCUIT DESIGN x y z F 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 Truth Table Boolean Function F = x + y’z x F y Logic Diagram z

  3. Design Logic Circuit using NAND gates only • E.g. 1: A + B’

  4. Design Logic Circuit using NAND gates only • E.g. 2: A’B + C

  5. Design Logic Circuit using NAND gates only • E.g. 3: [(A + B) . C]’’

  6. Half Adder circuit • To understand what is a half adder you need to know what is an adder first. • Adder circuit is a combinational digital circuit that is used for adding two numbers. A typical adder circuit produces a sum bit (denoted by S) and a carry bit (denoted by C) as the output. • Besides addition, adder circuits can be used for a lot of other applications in digital electronics like address decoding, table index calculation etc. • Adder circuits are of two types: Half adder and Full adder.

  7. Half Adder circuit • Half adder is a combinational arithmetic circuit that adds two numbers and produces a sum bit (S) and carry bit (C) as the output. • The arithmetic operation, addition of two binary digits has four possible elementary operations, namely: • 0 + 0 = 0 • 0 + 1 = 1 • 1 + 0 = 1 • 1 + 1 = 0 with 1 carry • If  A and B are the input bits, then sum bit (S) is the X-OR of A and B and the carry bit (C) will be the AND of A and B. • From this it is clear that a half adder circuit can be easily constructed using one X-OR gate and one AND gate.

  8. Half Adder circuit • Inputs: A + B • Outputs: Sum (S) , Carry (C) Boolean Expressions: Sum (S) = A’B + AB’ Carry (C) = AB Logic Circuit Truth Table

  9. Half Subtractor circuit • Half Subtractor is a combinational circuit that performs subtraction of two bits and has two inputs and two outputs. • The two inputs denoted by A and B represents minuend and subtrahend. • The two outputs are the difference “D” and the borrow bit “Bo“.

  10. Half Subtractor circuit • Half Subtractor is a combinational circuit that performs subtraction of two bits and has two inputs and two outputs. • The two inputs denoted by A and B represents minuend and subtrahend. • The two outputs are the difference “D” and the borrow bit “Bo“. Boolean Expressions: Difference (D) = A’B + AB’ Borrow (B0) = A’B Truth Table Logic Circuit

  11. Multiplexer • A multiplexer has many input lines and one output line. • The signal from one input line will be directed to the output line. • The input line is chosen based on the signals which are carried to the multiplexer on another set of input lines called control lines. • Multiplexers are sometimes called selectors because they choose or select one of their inputs. • The number of control lines needed depends on the number of input lines. • A multiplexer with 2 control lines can select from 4 input lines, a multiplexer with 3 control lines can select from 8 input lines. • In general, a multiplexer with n control lines can select from up to 2ninput lines.

  12. Multiplexers • 4-to-1 multiplexer

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