Chapter ObjeCtives
After studying this chapter, you will be able to:
• Determine whether a given mathematical structure is a Boolean algebra.
• Prove properties about Boolean algebras.
• Understand what it means for an isomorphism function to preserve the effects
of a binary operation or other property.
• Draw a logic network to represent a Boolean expression.
• Write a Boolean expression to represent a logic network.
• Write the truth function for a Boolean expression or logic network.
• Write a Boolean expression in canonical sum-of-products form for a given
truth function.
• Use NAND and NOR gates as well as AND, OR, and NOT gates to build logic
networks.
• Write a truth function from a description of a logical control device.
• Simplify Boolean expressions and logic networks using Karnaugh maps.
• Simplify Boolean expressions and logic networks using the Quine–McCluskey
method.
You have been hired by Rats R Us to build the control logic for the production facilities
for a new anticancer chemical compound being tested on rats. The control logic must
manage the opening and closing of two valves, A and B, downstream of the mixing
vat. Valve A is to open whenever the pressure in the vat exceeds 50 psi (pounds per
square inch) and the salinity of the mixture exceeds 45 g/L (grams per liter). Valve B is
to open whenever valve A is closed and the temperature exceeds 53°C and the acidity
falls below 7.0 pH (lower pH values mean more acidity).
Question: How many and what type of logic gates will be needed in the circuit?
The answer to this electronics problem lies, surprisingly, in a branch of mathematics developed around 1850 by George Boole, an English mathematician.
Boole was interested in developing rules of “algebra” for logical thinking,
similar to the rules of algebra for numerical thinking. Derided at the time as
useless, if harmless, Boole’s work is the foundation for the electronics found in
computers today.
8 8
Boolean Algebra and
Computer Logic
C h a p t e r
617
After studying this chapter, you will be able to:
• Determine whether a given mathematical structure is a Boolean algebra.
• Prove properties about Boolean algebras.
• Understand what it means for an isomorphism function to preserve the effects
of a binary operation or other property.
• Draw a logic network to represent a Boolean expression.
• Write a Boolean expression to represent a logic network.
• Write the truth function for a Boolean expression or logic network.
• Write a Boolean expression in canonical sum-of-products form for a given
truth function.
• Use NAND and NOR gates as well as AND, OR, and NOT gates to build logic
networks.
• Write a truth function from a description of a logical control device.
• Simplify Boolean expressions and logic networks using Karnaugh maps.
• Simplify Boolean expressions and logic networks using the Quine–McCluskey
method.
You have been hired by Rats R Us to build the control logic for the production facilities
for a new anticancer chemical compound being tested on rats. The control logic must
manage the opening and closing of two valves, A and B, downstream of the mixing
vat. Valve A is to open whenever the pressure in the vat exceeds 50 psi (pounds per
square inch) and the salinity of the mixture exceeds 45 g/L (grams per liter). Valve B is
to open whenever valve A is closed and the temperature exceeds 53°C and the acidity
falls below 7.0 pH (lower pH values mean more acidity).
Question: How many and what type of logic gates will be needed in the circuit?
The answer to this electronics problem lies, surprisingly, in a branch of mathematics developed around 1850 by George Boole, an English mathematician.
Boole was interested in developing rules of “algebra” for logical thinking,
similar to the rules of algebra for numerical thinking. Derided at the time as
useless, if harmless, Boole’s work is the foundation for the electronics found in
computers today.
8 8
Boolean Algebra and
Computer Logic
C h a p t e r
617