1. Multiplexers XOR 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 sources to a destination. e.g., processor’s registers to ALU

3. Multiplexers

4. 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

5. 74x151 8-input multiplexer

6. 74x151 truth table

7. 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 =

8. 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 =

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 = 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.

20. Multiplexers, Demultiplexers, and Buses

21. 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)