Ee121 john wakerly lecture 6
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EE121 John Wakerly Lecture #6. Adders Multipliers Read-Only Memories Barrel-Shifter Design Example. 4-bit comparator. EQ_L. Equality Comparators. 1-bit comparator. 8-bit Magnitude Comparator. Other conditions. Comparators in ABEL. Equality checking PEQQ = ([P7..P0] == [Q7..Q0]);

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EE121 John Wakerly Lecture #6

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Ee121 john wakerly lecture 6

EE121 John Wakerly Lecture #6

Adders

Multipliers

Read-Only Memories

Barrel-Shifter Design Example


Equality comparators

  • 4-bit comparator

EQ_L

Equality Comparators

  • 1-bit comparator


8 bit magnitude comparator

8-bit Magnitude Comparator


Other conditions

Other conditions


Comparators in abel

Comparators in ABEL

  • Equality checking

    • PEQQ = ([P7..P0] == [Q7..Q0]);

    • PEQQ_L = !([P7..P0] == [Q7..Q0]);

    • 16 product terms

  • Magnitude comparison

    • PGTQ = ([P7..P0] > [Q7..Q0]);

    • PGTQ_L = !([P7..P0] > [Q7..Q0]);

    • 255 product terms (try it in Foundation!)


Adders

XYCinSCout

00000

00110

01010

01101

10010

10101

11001

11111

Adders

  • Basic building block is “full adder”

    • 1-bit-wide adder, produces sum and carry outputs

  • Truth table:


Full adder circuit

Full-adder circuit


Ripple adder

Ripple adder

  • Speed limited by carry chain

  • Faster adders eliminate or limit carry chain

    • 2-level AND-OR logic ==> 2n product terms

    • 3 or 4 levels of logic, carry lookahead


74x283 4 bit adder

74x2834-bit adder

  • Uses carry lookahead internally


Ee121 john wakerly lecture 6

“generate”

“half sum”

carry-in from previous stage

“propagate”


Ripple carry between groups

Ripple carry between groups


Lookahead carry between groups

Lookahead carry between groups


Addition in abel

Addition in ABEL

  • Easy?

    • No -- huge number of product terms!

    • On the order of 2n for bit n

    • @CARRY directive


Subtraction

Subtraction

  • Subtraction is the same as addition of the two’s complement.

  • The two’s complement is the bit-by-bit complement plus 1.

  • Therefore, X – Y = X + Y + 1 .

    • Complement Y inputs to adder, set Cin to 1.

    • For a borrow, set Cin to 0.


Full subtractor full adder almost

Full subtractor = full adder, almost


Multipliers

Multipliers

  • 8x8 multiplier


4x4 multiplier in abel

4x4 multiplier in ABEL


Full adder array

Full-adder array


Faster carry chain

Faster carry chain


Read only memories

Read-Only Memories


Why rom

Why “ROM”?

  • Program storage

    • Boot ROM for personal computers

    • Complete application storage for embedded systems.

  • Actually, a ROM is a combinational circuit, basically a truth-table lookup.

    • Can perform any combinational logic function

    • Address inputs = function inputs

    • Data outputs = function outputs


Logic in rom example

Logic-in-ROM example


4x4 multiplier example

4x4 multiplier example


Internal rom structure

Internal ROM structure

PDP-11 boot ROM

(64 words, 1024 diodes)


Two dimensional decoding

Two-dimensional decoding

?


Larger example 32kx8 rom

Larger example, 32Kx8 ROM


Today s roms

Today’s ROMs

  • 256K bytes, 1M byte, or larger

  • Use MOS transistors


Eeproms flash proms

EEPROMs, Flash PROMs

  • Programmable and erasableusing floating-gate MOS transistors


Typical commercial eeproms

Typical commercial EEPROMs


Eeprom programming

EEPROM programming

  • Apply a higher voltage to force bit change

    • E.g., VPP = 12 V

    • On-chip high-voltage “charge pump” in newer chips

  • Erase bits

    • Byte-byte

    • Entire chip (“flash”)

    • One block (typically 32K - 66K bytes) at a time

  • Programming and erasing are a lot slower than reading (milliseconds vs. 10’s of nanoseconds)


Microprocessor eprom application

Microprocessor EPROM application


Rom control and i o signals

ROM control and I/O signals


Rom timing

ROM timing


Next time

Next time

  • Sequential circuits (Chapter 7)


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