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Multiplexers XOR gates

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.

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Multiplexers XOR gates

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  1. MultiplexersXOR gates

  2. 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 sourcesto a destination. e.g., processor’s registers to ALU

  3. Multiplexers

  4. 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 sourcesto a destination. e.g., processor’s registers to ALU

  5. 74x1518-input multiplexer

  6. 74x151 truth table

  7. Multiplexers n-1 EN . Mj .iDj iY = j = 0 • 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.

  8. 4-input, 1-bit Multiplexer 3 EN . Mj .iDj Y = j = 0 • 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.

  9. CMOS transmission gates • 2-input multiplexer

  10. Other multiplexer varieties • 2-input, 4-bit-wide • 74x157 • 4-input, 2-bit-wide • 74x153

  11. Multiplexers

  12. ABEL code for 74x153-like mux

  13. Easier ABEL multiplexer code

  14. 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

  15. 16 16-to-1 muxes 16-to-1 mux = 2 x 74x151 8-to-1 mux + NAND gate

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

  17. Properties of different approaches

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

  19. 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.

  20. Multiplexers, Demultiplexers, and Buses

  21. 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.

  22. 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.

  23. 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’

  24. 2-input XOR gates XY = X’.Y + X.Y’

  25. Commercial chip • 74x86 • has four XOR gates

  26. 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.

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

  28. 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

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

  30. Parity tree • Faster with balanced tree structure

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

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