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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

EE121 John Wakerly Lecture #6

Adders

Multipliers

Read-Only Memories

Barrel-Shifter Design Example


Equality comparators

EQ_L

Equality Comparators

  • 1-bit comparator




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

X Y Cin S Cout

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Adders

  • Basic building block is “full adder”

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

  • Truth table:



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


“generate”

“half sum”

carry-in from previous stage

“propagate”




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.



Multipliers
Multipliers

  • 8x8 multiplier






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




Internal rom structure
Internal ROM structure

PDP-11 boot ROM

(64 words, 1024 diodes)




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



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)





Next time
Next time

  • Sequential circuits (Chapter 7)


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