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DDCA_Ch5

Chapter 5: Digital Building Blocks

5.1 Introduction

Key digital building blocks: Gates, Multiplexers, Decoders, Registers, Arithmetic Circuits, Counters, Memory Arrays, Logic Arrays.Characteristics:

  • Hierarchy: Comprised of simpler components.

  • Modularity: Operate independently with defined functions.

  • Regularity: Consistent structure for easy scaling.

5.2 Arithmetic Circuits
  • Half Adder:Inputs: A, B; Outputs: Sum (S), Carry out (Cout); Equations: S = A XOR B, Cout = A AND B.

  • Full Adder:Inputs: A, B, Cin; Outputs: S, Cout; Equations: S = A XOR B XOR Cin, Cout = (A AND B) OR (Cin AND (A XOR B)).

5.2.2 Types of Adders
  • Carry Propagate Adders (CPAs):

    • Ripple-Carry Adder: Slow, propagates carries through each bit.

    • Carry-Lookahead Adder: Faster, reduces propagation delay.

    • Prefix Adder: Fastest, groups to compute carries.

5.3 Sequential Building Blocks
  • Counters: Count in binary; applications include clocks and program counters.

  • Shift Registers: Handle serial/parallel data; act as converters or N-bit registers.

5.4 Memory Arrays
  • Types of memory:

    • Dynamic RAM (DRAM): Volatile, requires refresh.

    • Static RAM (SRAM): Faster, more expensive.

    • Read Only Memory (ROM): Non-volatile.

  • Structure: Organized as a 2D matrix of bit cells; addressing enables data access.

5.5 Logic Arrays
  • Programmable Logic Arrays (PLAs): AND followed by OR for combinational logic.

  • Field Programmable Gate Arrays (FPGAs): Logic elements and programmable interconnects for combinational and sequential logic.

5.6 Number Systems

Common representations include unsigned binary for positives and two's complement for negatives.

5.7 Shifters
  • Logical Shifter: Fills with zeros.

  • Arithmetic Shifter: Preserves sign bit.

  • Rotators: Circular shifts.

5.8 Floating-Point Representation

Defines real numbers using IEEE 754 standard (single and double precision). Components include sign bit, exponent, and mantissa. Key processes include normalization and rounding in arithmetic operations.

Key Concepts

ALUs form the core of processors, performing arithmetic and logical functions using various memory structures and logic circuits.