Multiplexers XOR gates

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

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

74x151 8-input multiplexer

74x151 truth table

Multiplexers iY is a particular output bit, Mj represents minterm j of the s select inputs; and iDj is the input bit i of source j; When the mutiplexer is enabled and the value on the select inputs is j, each output iY equals the corresponding bit of the selected input, iDj. n-1 j = 0 EN. M j. iDj iY =

4-input, 1-bit Multiplexer Y is the output bit, Mj represents minterm j (0~3) of the 2 select inputs; and Dj is the input bit of source j; When the mutiplexer is enabled and the value on the select inputs is j, the output Y equals the corresponding bit of the selected input, Dj. 3 j = 0 EN. M j. iDj Y =

CMOS transmission gates 2-input multiplexer

Other multiplexer varieties 2-input, 4-bit-wide –74x157 4-input, 2-bit-wide –74x153

Multiplexers

ABEL code for 74x153-like mux

Easier ABEL multiplexer code

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

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

Properties of different approaches

ABEL code for barrel shifter 20 inputs 16 outputs 16 product terms per output

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

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.

2-input XOR gates Like an OR gate, but excludes the case where both inputs are 1. XNOR: complement of XOR X  Y = X’.Y + X.Y’

2-input XOR gates X  Y = 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.

CMOS XOR with transmission gates IF B==1 THEN Z = !A; ELSE Z = A;

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

Multi-input XOR Sum modulo 2 Parity computation Used to generate and check parity bits in computer systems. –Detects any single-bit error

Parity tree Faster with balanced tree structure

Next time Comparators Adders Multipliers Read-only memories (ROMs)