CDA-4101 Lecture 8 Notes

"Hitting baseballs and writing software are two professions where you can become a millionaire with a 75% performance failure rate." - Unknown

• Similar to software design, electrical engineers need to build up abstractions and build systems using these abstractions.
• Just as programmers don't design with bits and bytes when they design complex software, electrical engineers do not use gates.
• Gates can be arranged to form modules that serve a specific function.
• These modules serve as abstractions and are building blocks more more complex modules.

• multiple gates are put onto Integrated Circuits (ICs)
• dual inline packages (DIPS) have a particular form factor with two rows of pins.
• number of pins of a DIP vary
• there are other packaging types that allow larger chips and/or more pins
• pins have power, ground, inputs, outputs
• notches indicate orientation
• chips, ICs, DIPS, etc. are terms often used interchangably (which is not technically correct)

74LS00 - 2-input NAND (X4) 74LS04 - 1-input NOT (X6) 74LS08 - 2-input AND (X4) 74LS32 - 2-input OR (X4)

74LS00

• SSI (Small Scale Integration) - 1 to 10 gates
• MSI (Medium Scale Integration) - 10 to 100 gates
• LSI (Large Scale Integration) - 100 to 100,000 gates
• VLSI (Very Large Scale Integration) - more than 100,000 gates

Used to build computers out of many SSIs, but now etch them all onto a single chip

• there is a gate delay, which impacts design decisions
• we will mostly ignore gate delays in our discussions
• number of gates on a chip is limited by the number of pins
• you can make a chip with 10 million NAND gates, but it will require 30,000,002 pins and thus need to be about 38 kilometers long
• want self-contained functional units, comprised of gates that have a hight ratio of gates to input pins

• a digital circuit where the outputs depend only on the current inputs is a combinational circuit
• alternate is that the output can depend on previous inputs (i.e., there is memory)
• all circuits we have so far developed and that are developed with Karnaugh maps are combinational circuits
• we are going to look a a few standard, useful combinational circuits

Function: To select one of several inputs to select one of 2n inputs you only need n lines to "select" the input to have an 8 input, m bit multiplexer just repeat with selection inputs going to each of m units

8 input, 1 bit multiplexer

• Aside from selection, any boolean function of three variables can easily be created with an 8 input MUX
• Just wire input Dn to Vcc if the n-th row of the truth table has a '1' and to ground otherwise

Majority Function truth table A B C M 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1

Majority Function using MUX

Majority Function direct implementation

Function: To direct input to one of several outputs

1 bit, 4 output demultiplexer

Function: To convert an "n"-bit binary encoded signal into logic '1' on one of 2n outputs This is a binary encoder In general an encoder takes and sort of code and outputs a code word (decoded)

2 input, 4 output decoder

F(X,Y,Z) = X' Y' Z' + X' Y Z' + X Y' Z' + X' Y Z'

• Making 32 MB of RAM from 8MB RAM modules

4 output decoder with ENABLE

4 output demultiplexer

• General Chip for Implementing boolean functions in sum-of-products forms.
• fusable links (X's) allow user to define inputs to AND gates and OR gates.
• limits:
  • number of inputs (complements generated internally)
  • number of AND gates (number of differnent product terms)
  • number of OR gates (number of functions)

Function: Determine if two bit strings are equal Symbol for XOR gate

4 bit Comparator

• Bit shifting used in lower-level programming
• why does the textbook include it in the "Artithmetic Circuits" subsection?
  • "1-bit left-shift" is equivalent to multiplying by 2
  • "1-bit right-shift" is equivalent to dividing by 2

• Not very efficient: need to wait for all carry bits to ripple through.
• The more bits you are adding the longer the delay
• carry lookahead or carry select adders are able to eliminate most of the ripple carry delays

Multi-bit ALUs can be made by stringing these together with common function selection lines and ripple carry bits

Func. Sel, ALU F0 F1 Function 0 0 A AND B 0 1 A OR B 1 0 NOT B 1 1 A + B