Introduction to Digital Computers

• 1 The digital abstraction
  • Transistors, From analog signals to digital signals
  • Transfer functions of gates, The bounded-noise model
  • The digital abstraction in presence of noise
  • Stable signals
• 2 Foundations of combinational circuits
  • Boolean functions
  • Gates as implementations of Boolean functions
  • Building blocks , Combinational circuits
  • Cost and propagation delay , Syntax and semantics
• 3 Trees
  • Trees of associative Boolean gates
  • Optimality of trees
• 4 Decoders and Encoders
  • Notation, Values represented by binary strings
  • Decoders
• 5 Combinational modules
  • Multiplexers, Cyclic Shifters, Priority Encoders
  • Half-Decoders, Logical Shifters
• 6 Addition
  • Denition of a binary adder, Ripple Carry Adder
  • Carry bits, Conditional Sum Adder, Compound Adder
• 7 Fast Addition
  • Reduction: sum-bits 7

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