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CH 03 : Logic Gates And Logic Circuits

Logic Gates

  • Logic Gates: They take binary inputs and give binary outputs in an electronic circuit.

  • Truth Table: A table used to check the outputs from a logic gate or logic circuit.

    • All possible combinations of binary inputs are considered in a Truth Table.

  • The six different types of Logic Gates are as follows:

  • NOT Gate: Has only one input and output is 1 only if input is 0.

    • Truth Table:

Input

Output

A

X

0

1

1

0

  • AND Gate: Two inputs. Output is 1 if both inputs are 1s.

    • Truth Table:

Input

Input

Output

A

B

X

0

1

0

1

0

0

0

0

0

1

1

1

  • Tip: Multiply the inputs.

  • OR Gate: Two inputs. Output is 1 when any of the inputs is 1.

    • Truth Table:

Input

Input

Output

A

B

X

0

1

1

1

0

1

0

0

0

1

1

1

  • Tip: Add the inputs.

  • NAND (NOT AND) Gate: Two Inputs. Output is 1 if both inputs are not 1.

    • Truth Table:

Input

Input

Output

A

B

X

0

1

1

1

0

1

0

0

1

1

1

0

  • Tip: Calculate for AND and write opposite output.

  • NOR (NOT OR) Gate: Two inputs. Output is 1 if neither input is 1

    • Truth Table:

Input

Input

Output

A

B

X

0

1

0

1

0

0

0

0

1

1

1

0

  • Tip: Calculate for OR and write opposite.

  • XOR Gate: Two inputs. Output is 1 if inputs are not same.

    • Truth Table:

Input

Input

Output

0

1

1

1

0

1

0

0

0

1

1

0


Logic Circuits

  • Multiple Logic gates make up a Logic Circuit.

  • Complex operations are performed through them.

  • Truth tables are made to check outputs, and all inputs are considered.

  • To make a truth table, it is easier to divide the circuit into parts and name all the outputs at each stage.Example:

Input A

Input B

Input C

Output P

Output Q

Output R

Output X

0

0

0

0

1

1

1

0

0

1

0

0

0

1

0

1

0

0

0

0

0

0

1

1

0

0

0

1

1

0

0

0

1

1

1

1

0

1

0

0

0

1

1

1

0

1

0

1

1

1

1

1

1

0

1

0

  • In order to make a Logic Circuit from a Logic statement, mark all the gates in the statement, and always mind the brackets.

  • To make a logic circuit from Boolean or Logic statements, make different parts of the circuit and then join them using gates which connect the brackets.

  • Some logic gates can make a whole logic circuit and any other logic gate. They are known as Building Blocks. NAND gate, for example, can make an AND gate:

  • Logic circuit can also be simplified. Just like the circuit above can be simplified to just one AND gate.

  • Note: When one input branches into two before entering a gate, the two branched inputs will always be same. 1,1 or 0,0.

CH 03 : Logic Gates And Logic Circuits

Logic Gates

  • Logic Gates: They take binary inputs and give binary outputs in an electronic circuit.

  • Truth Table: A table used to check the outputs from a logic gate or logic circuit.

    • All possible combinations of binary inputs are considered in a Truth Table.

  • The six different types of Logic Gates are as follows:

  • NOT Gate: Has only one input and output is 1 only if input is 0.

    • Truth Table:

Input

Output

A

X

0

1

1

0

  • AND Gate: Two inputs. Output is 1 if both inputs are 1s.

    • Truth Table:

Input

Input

Output

A

B

X

0

1

0

1

0

0

0

0

0

1

1

1

  • Tip: Multiply the inputs.

  • OR Gate: Two inputs. Output is 1 when any of the inputs is 1.

    • Truth Table:

Input

Input

Output

A

B

X

0

1

1

1

0

1

0

0

0

1

1

1

  • Tip: Add the inputs.

  • NAND (NOT AND) Gate: Two Inputs. Output is 1 if both inputs are not 1.

    • Truth Table:

Input

Input

Output

A

B

X

0

1

1

1

0

1

0

0

1

1

1

0

  • Tip: Calculate for AND and write opposite output.

  • NOR (NOT OR) Gate: Two inputs. Output is 1 if neither input is 1

    • Truth Table:

Input

Input

Output

A

B

X

0

1

0

1

0

0

0

0

1

1

1

0

  • Tip: Calculate for OR and write opposite.

  • XOR Gate: Two inputs. Output is 1 if inputs are not same.

    • Truth Table:

Input

Input

Output

0

1

1

1

0

1

0

0

0

1

1

0


Logic Circuits

  • Multiple Logic gates make up a Logic Circuit.

  • Complex operations are performed through them.

  • Truth tables are made to check outputs, and all inputs are considered.

  • To make a truth table, it is easier to divide the circuit into parts and name all the outputs at each stage.Example:

Input A

Input B

Input C

Output P

Output Q

Output R

Output X

0

0

0

0

1

1

1

0

0

1

0

0

0

1

0

1

0

0

0

0

0

0

1

1

0

0

0

1

1

0

0

0

1

1

1

1

0

1

0

0

0

1

1

1

0

1

0

1

1

1

1

1

1

0

1

0

  • In order to make a Logic Circuit from a Logic statement, mark all the gates in the statement, and always mind the brackets.

  • To make a logic circuit from Boolean or Logic statements, make different parts of the circuit and then join them using gates which connect the brackets.

  • Some logic gates can make a whole logic circuit and any other logic gate. They are known as Building Blocks. NAND gate, for example, can make an AND gate:

  • Logic circuit can also be simplified. Just like the circuit above can be simplified to just one AND gate.

  • Note: When one input branches into two before entering a gate, the two branched inputs will always be same. 1,1 or 0,0.

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