Multiplexers

DeMultiplexers XOR gates

Multiplexers

• A multiplexer is a digital switch - it connects data from one of n sources to its output.

Data Selectors

• Multiplexers also known as Data Selectors

Multiplexers

• An n-input and b-bit multiplexer has n soureces of data, each of which b bits wide, and there are b output bits.

• A multiplexer is a unidirectional device.

• Multiplexers are used in any application in which data must be switched from multiple sources to a destination.

e.g., processor’s registers to ALU

Multiplexers

74x1518-input 1-bit multiplexer

Multiplexers74x151

8-input, 1-bit-wide Multiplexer8-input, 1-bit Multiplexer1-bit, 8-to-1 Multiplexer1, 8-to-1 Multiplexer1, 1-of-8 Data SelectorSingle, 1-of-8 Data Selector

74x1572-input, 4-bit-wide Multiplexer2-input, 4-bit Multiplexer4-bit, 2-to-1 Multiplexer4, 2-to-1 MultiplexerQuadruple 2-line to 1-line Data Selector/Multiplexer Quad, 1-of-2 Data Selector

74x1534-input, 2-bit-wide Multiplexer2-bit, 4-to-1 Multiplexer2, 1-of-4 Data Selector

74x151 truth table

Other multiplexer varieties

• 2-input, 4-bit-wide– 74x157

• 4-input, 2-bit-wide– 74x153

Multiplexers• Describe:

16 16-to-1 muxes

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

4 16-bit 2-to-1 muxes

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

Multiplexers, Demultiplexers• A multiplexer is used to select one of n sources of data to

transmit on a bus.

• A demultiplexer is opposite of a multiplexer.

• A 1-bit, n-output demultiplexer has one data input and s inputs to select one of n = 2s data outputs.

• A b-bit, n-output demultiplexer has b-data input and s inputs to select one of n = 2s sets of b-data outputs.

Multiplexers, Demultiplexers, and Buses

Multiplexers, Demultiplexers, and Buses• A multiplexer can be used to select one of n sources of data

to transmit on a bus.• A demultiplexer can be used to route the bus data to one of

m destinations.

Decoder/Demultiplexers• A binary decoder with an enable input can be used as a

demultiplexer.• The decoder’s enable input is connected to the data line, and

its select inputs determine which of its output lines is driven with the data bit.

Binary 2-to-4 decoder

Note “x” (don’t care) notation.

2-input XOR gates• Like an OR gate, but excludes the case where both inputs

are 1.

• XNOR: complement of XOR

XY = X’.Y + X.Y’

2-input XOR gatesXY = X’.Y + X.Y’

Commercial chip• 74x86• has four XOR gates

XOR and XNOR symbols• The logic symbols for XOR and XNOR functions are shown

below. • There are four equivalent symbols for each function.

• All of these alternatives are a consequence of a simple rule:

any two signals (inputs or output) of an XOR or XNOR gate may be complemented without changing the resulting logic function.

Multi-input XOR• n XOR gates may be connected to form a circuit with n+1

inputs and a single output.• This is called an odd-parity circuit, because its output is 1 if

an odd number of inputs are 1.

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

Parity tree• Faster with balanced tree structure