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EE121 John Wakerly Lecture #6

Three-state Outputs

Encoders

Multiplexers

XOR gates

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Three-state buffers

• Output = LOW, HIGH, or Hi-Z.

• Can tie multiple outputs together, if at most one at a time is driven.

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Different flavors

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Timing considerations

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Three-state drivers

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Driver application

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Three-state transceiver

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Transceiver application

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Three-state enables in ABEL

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Encoders vs. Decoders

Decoder Encoder

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Binary encoders

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Need priority in most applications

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8-input priority encoder

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Priority-encoder logic equations

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74x148 8-input priority encoder

– Active-low I/O– Enable Input– “Got Something”– Enable Output

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74x148circuit

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74x148 Truth Table

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Cascading priority encoders

• 32-inputpriority encoder

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15-input priority encoder in ABEL

• Declarations

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Constant expressions

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Outputs

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Alternative formulation

• WHEN is very natural for priority function

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Multiplexers

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74x1518-input

multiplexer

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74x151 truth table

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CMOS transmission gates

• 2-input multiplexer

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Other multiplexer varieties

• 2-input, 4-bit-wide– 74x157

• 4-input, 2-bit-wide– 74x153

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ABEL code for 74x153-like mux

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Easier ABEL multiplexer code

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Barrel shifter design example

• n data inputs, n data outputs• Control inputs specify number of positions to

rotate or shift data inputs• Example: n = 16

– DIN[15:0], DOUT[15:0], S[3:0] (shift amount)

• Many possible solutions, all based on multiplexers

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16 16-to-1 muxes

16-to-1 mux = 2 x 74x151 8-to-1 mux + NAND gate

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4 16-bit 2-to-1 muxes

16-bit 2-to-1 mux = 4 x 74x157 4-bit 2-to-1 mux

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Properties of different approaches

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ABEL code for barrel shifter

20 inputs16 outputs16 product terms per output

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2-input XOR gates

• Like an OR gate, but excludes the case where both inputs are 1.

• XNOR: complement of XOR

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XOR and XNOR symbols

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Gate-level XOR circuits

• No direct realization with just a few transistors.

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CMOS XOR with transmission gates

IF B==1 THEN Z = !A;ELSE Z = A;

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Multi-input XOR

• Sum modulo 2• Parity computation

• Used to generate and check parity bits in computer systems.– Detects any single-bit error

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Parity tree

• Faster with balanced tree structure

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Next time

• Comparators• Adders• Multipliers• Read-only memories (ROMs)