Logic Gates

Section 11.1 Logic Gates

Logic gates are the foundation of digital circuits. They process binary inputs to produce specific outputs. The basic logic gates are

A N D,

O R,

and

N O T .

Derived gates include

N A N D,

N O R,

X O R,

and

X N O R .

Each gate has its own symbol and behavior defined by a truth table.

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Subsection 11.1.1 AND Gate

The AND gate produces a 1 only when both inputs are 1.

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from sympy.logic.boolalg import And
from sympy.abc import A, B
And(A, B)

Truth table for the AND gate:

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# Generate truth table for AND gate
print("\nA | B | A AND B")
print("--|---|--------")
for A in [False, True]:
    for B in [False, True]:
        print(f"{int(A)} | {int(B)} | {int(bool(And(A, B)))}")

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Subsection 11.1.2 OR GATE

The OR gate produces a 1 if at least one input is 1.

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from sympy.logic.boolalg import Or
from sympy.abc import A, B
Or(A, B)

Truth table for the OR gate:

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# Generate truth table for OR gate
print("\nA | B | A OR B")
print("--|---|--------")
for A in [False, True]:
    for B in [False, True]:
        print(f"{int(A)} | {int(B)} | {int(bool(Or(A, B)))}")

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Subsection 11.1.3 NOT Gate

The NOT gate inverts the input: 1 becomes 0, and 0 becomes 1.

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from sympy.logic.boolalg import Not
from sympy.abc import A
Not(A)

Truth table for the NOT gate:

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# Generate truth table for NOT gate
print("\nA | NOT A")
print("--|-------")
for A in [False, True]:
    print(f"{int(A)} | {int(bool(Not(A)))}")

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Subsection 11.1.4 NAND Gate

NAND: Produces 0 only when both inputs are 1.

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Subsection 11.1.5 NOR Gate

NOR: Produces 1 only when both inputs are 0.

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Subsection 11.1.6 XOR Gate

XOR: Produces 1 when inputs differ.

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Subsection 11.1.7 XNOR Gate

XNOR: Produces 1 when inputs are the same.

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from sympy.logic.boolalg import And, Or, Not, Xor
​
def nand(A, B):
    return Not(And(A, B))
​
def nor(A, B):
    return Not(Or(A, B))
​
def xor(A, B):
    return Xor(A, B)
​
def xnor(A, B):
    return Not(Xor(A, B))
​
# User-defined inputs
A = 1 # Replace with 0 or 1 for input A
B = 0 # Replace with 0 or 1 for input B
gate = "xor" # Replace with "nand", "nor", "xor", or "xnor"
​
​
if gate == "nand":
    result = nand(A, B)
elif gate == "nor":
    result = nor(A, B)
elif gate == "xor":
    result = xor(A, B)
elif gate == "xnor":
    result = xnor(A, B)
else:
    result = "Invalid gate type! Please use 'nand', 'nor', 'xor', or 'xnor'."
​
result

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