Chapter 5: Digital Building Blocks

5.1 Introduction

• Digital building blocks include:

  • Gates

  • Multiplexers

  • Decoders

  • Registers

  • Arithmetic Circuits

  • Counters

  • Memory Arrays

  • Logic Arrays

• Characteristics of digital building blocks:

  • Hierarchy: Comprised of simpler components.

  • Modularity: Each block operates independently with well-defined functions.

  • Regularity: Structure is consistent, allowing easy scaling in size.

5.2 Arithmetic Circuits

5.2.1 Adders

• Half Adder:

  • Inputs: A, B

  • Outputs: Sum (S), Carry out (Cout)

  • Boolean equations:

    • S = A XOR B

    • Cout = A AND B

• Full Adder:

  • Inputs: A, B, Carry in (Cin)

  • Outputs: Sum (S), Carry out (Cout)

  • Boolean 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, carries ripple through each bit.

  • Carry-Lookahead Adder: Faster, reduces carry propagation delay by generating carry directly.

  • Prefix Adder: Fastest, relies on grouping to compute carries.

5.3 Sequential Building Blocks

5.3.1 Counters

• Count in binary sequence on clock edges.

• Applications include digital clocks, program counters.

5.3.2 Shift Registers

• Serial-in, serial-out or parallel-in, parallel-out data handling.

• Can act as a serial-to-parallel converter or a normal N-bit register if loaded.

5.4 Memory Arrays

• Types of memory:

  • Dynamic RAM (DRAM): Volatile memory, needs periodic refresh.

    • Invented in 1966 by Robert Dennard at IBM.

  • Static RAM (SRAM): Uses flip-flops, faster than DRAM but more expensive.

  • Read Only Memory (ROM): Non-volatile, retains data without power.

5.4.1 Memory Structure

• Memory array organized as a two-dimensional matrix of bit cells.

  • Each cell stores one bit.

  • Addressing allows access to different cells to read/write data.

5.5 Logic Arrays

• Programmable Logic Arrays (PLAs):

  • Composed of an AND array followed by an OR array.

  • Used for combinational logic.

• Field Programmable Gate Arrays (FPGAs):

  • Composed of logic elements and programmable interconnections.

  • Can implement both combinational and sequential logic.

5.6 Number Systems

• Binary Representation: Used for positive and negative numbers.

  • Unsigned binary: Represents positive numbers only.

  • Two's complement: Used for negative numbers representation.

5.7 Shifters

• Logical Shifter: Shifts bits left or right, filling empty bits with zeros.

• Arithmetic Shifter: Shifts while preserving the sign bit (for right shifts).

• Rotators: Circular shifts of bit patterns.

5.8 Floating-Point Representation

• Used to represent real numbers with fractions.

• IEEE 754 Standard: Defines single-precision (32-bit) and double-precision (64-bit).

• Components:

  • Sign bit: Indicates number sign.

  • Exponent: Adjusts range.

  • Mantissa: Represents significant digits.

Key Concepts and Examples

• Example of Floating-Point Number Representation:

  • Conversion from decimal to binary and filling IEEE 754.

  • Example of addition in floating-point format with normalization and rounding rules.

Practical Applications

• ALUs (Arithmetic Logic Units): Combine functional blocks to form the core of processors.

  • Operate on binary data, perform arithmetic and logical functions.

• Examples of Logic Circuits:

  • Use of ROMs and memory arrays to construct various logic functions.

This overview consolidates the digital building blocks detailed in Chapter 5, offering insights into various circuits, memory structures, and operational principles, which are crucial for understanding digital logic design.