<aside> 📌 Sommaire

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Module objectives

• Master the essential techniques of optimisation of programmable components
• Apply the critical rules in logic circuit design
• Describe, simulate and synthesise a combinatorial and sequential system using the VHDL
• Configure an FPGA and know the different steps of an EDA tool
• Distinguish the use cases of a programmable component from CPU/GPU/ASIC/MCU
• Design and analyse a logic circuit (sequential and combinatorial) and a state graph and then perform simulations and syntheses on a programmable component

From digital systems to components with programmable architectures

Reminders

Combinatorial versus sequential

• One does not imply feedback in the operations of the circuit, whereas the other does
• Combinatorial logic
  • At time T, outputs of the system depend on the entries at time T only
• Sequential logic
  • At time T, the outputs of the system depend on the entries at time T and the entries from previous moments

Main combinatorial functions

• Combinatorial logic
  • logical states, variables, functions: In digital logic, a logical state represents one of the possible values of a logical variable, typically binary (0 or 1). Logical functions then compute outputs based on the values of logical variables using Boolean algebra.
  • Logical/boolean operations: These follow the rules of Boolean algebra, dealing with binary variables and including operations like AND, OR, NOT, etc.
  • Coding tensions: This refers to the representation of logical states (0 and 1) with specific voltage levels in a circuit. For example, 0V might represent a logical 0, and 5V might represent a logical 1.
  • Positive/negative logic: Positive logic assigns a higher voltage level to a logical one and a lower voltage level to a logical 0. Negative logic does the opposite.
  • High/low levels: These terms refer to the voltage levels representing logical 1 (high) and logical 0 (low).
• Combinatorial functions
  • Basic logic gates like Not, And, Or, Nand, Nor, Xor, and Xnor each perform a specific Boolean operation. For example, an AND gate outputs one only if all its inputs are 1.
• Boolean algebra
  • Principles such as Involution, Commutativity, Associativity, Distributivity, Idempotence, Complementarity, Neutral Elements, and Absorption govern the simplification and manipulation of Boolean expressions.
• Algebraic expressions
  • Representations of the logical functions in terms of algebraic equations following Boolean algebra rules.
• Truth tables
  • Tables describe the logical function of a gate or circuit by listing all possible input combinations and their corresponding outputs.