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Microprocessors vs. Custom Digital Circuits

Understand the advantages of off-the-shelf microprocessors and the reasons behind designing custom digital circuits. Explore combinational logic circuits, Boolean algebra, logic gates, and their practical applications in system design.

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Microprocessors vs. Custom Digital Circuits

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  1. Microprocessors vs. Custom Digital Circuits Designers that work with digital phenomena often buy an off-the-shelf microprocessor and program it. Microprocessors are readily available, inexpensive, easy to program, and easy to reprogram Why would anyone ever need to design new digital circuits?

  2. Microprocessors vs. Custom Digital Circuits Designers that work with digital phenomena often buy an off-the-shelf microprocessor and program it. Microprocessors are readily available, inexpensive, easy to program, and easy to reprogram Why would anyone ever need to design new digital circuits? • Microprocessors are sometimes: • Too slow; • Too big; • Consume too much power; • Too costly

  3. Combinatorial Logic Circuits A digital circuit whose output depends solely on the present combination of input values is called a combinatorial circuit Logic gates – building blocks of logic circuits AND OR NOT Boolean Algebra Boolean algebra is a branch of mathematics that uses variables whose values can only be 1 or 0 (“true” or “false”, respectively) and whose operators, like AND, OR, NOT, operate on such variables and return 1 or 0. We can build circuits by doing math

  4. Logic Gates Truth Tables Example: Seatbelt warning light Design a system for an automobile that illuminates a warning light whenever the driver’s seatbelt is not fastened, and the key is in the ignition Boolean equation: w = NOT(s) AND k

  5. Notation and Terminology • Operators: • NOT(a) is typically written as a’ • a OR b is typically written as a + b • a AND b is typically written as a * b (or a b) w = NOT(s) AND k = s’k • Precedence rule: • Expression in parentheses • AND, NOT • OR w = (a + b) * (c’) + d

  6. Properties of Boolean Algebra • Commutative • a + b = b + a • a * b = b * a • Distributive • a * (b + c) = a * b + a * c • a + (b * c) = (a + b) * (a + c) • Associative • (a + b) + c = a + (b + c) • (a * b) * c = a * (b * c) • Identity • 0 + a = a + 0 = a • 1 * a = a * 1 = a • Complement • a + a’ = 1 • a * a’ = 0

  7. Additional Properties • Null elements • a + 1 = 1 • a * 0 = 0 • Idempotent Law • a + a = a • a * a = a • Involution Law • (a’)’ = a • De Morgan’s Law • (a + b)’ = a’ b’ • (a b)’ = a’ + b’ Example: Simplification of an automatic sliding door system f = h c’ + h’ p c’

  8. Additional Properties • Null elements • a + 1 = 1 • a * 0 = 0 • Idempotent Law • a + a = a • a * a = a • Involution Law • (a’)’ = a • De Morgan’s Law • (a + b)’ = a’ b’ • (a b)’ = a’ + b’ Example: Simplification of an automatic sliding door system f = h c’ + h’ p c’ f = c’ (h + p)

  9. Boolean Functions Boolean function is a mapping of each possible combination of input values to either 0 or 1. Boolean function can be represented as an equation, a circuit, and as a truth table. Converting a truth table to an equation F = a b + a’ F = a’ b’ + a’ b + a b For any function, there may be many equivalent equations, and many equivalent circuits, but there is only one truth table!

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