Question

 For this lab, design, synthesize, and functionally verify a 5x1 one-bit multiplexer circuit that is controlled by switches and drives an LED. In the design, use the switches and LED as indicated below

 . SW9-SW5 for the five data inputs with SW5 corresponding to select input "000"

 . SW3-SW1 for the select inputs

 . LEDS for the output of the multiplexer

 The value of each input must be indicated by the LED being ON or OFF. The corresponding output must be controlled by the select inputs. The binary decoder must be designed with the outputs of this decoder feeding the internal logic of the multiplexer that controls which of the five inputs is passed to the single output LED. Determine the Boolean equations for each output of the decoder and label using DO - D4. Also determine the Boolean equation for the multiplexer output knowing that only one decoder output is active at one time. No modules from the IP catalog can be used, only basic logic gates.

 Make sure to compare the simulation results, the Boolean expressions, and the truth tables with the development board functionality. Use the Waveform Viewer for functional verification and physically test using the DE10-Lite development board.

 Note:

 1. The Boolean equation for the multiplexer output indicates which data input is passed to the output. No Karnaugh map is required.

 2. The output of the multiplexer must be LOW "O" if an appropriate data input is not selected.

Answer 1

Multiplexer:

The term 'Multiplex' means "many to one".Multiplexing is the process of transmiting a large number of information over a single line. The multiplexer has several data-input lines and single lin. The selection of a prticular input line is controlled by a set of selection lines.The multiplexer, shortened to “MUX” or “MPX”, is a combinational logic circuit designed to switch one of several input lines through to a single common output line by the application of a control signal.

Binary Decoder

The Binary Decoder is a device that accepts a digital input (in binary form) and it activates one of its outputs. This device has several outputs, and the one that is activated is chosen by the code applied to the inputs. We can obtain 2ⁿ possible combinations with an n-bit code.Binary decoder converts a definite sequence of input bits into a specific pattern as decided by the user based on the requirement.

No they not Same cercuit. They have many differences like

Multiplexer	Binary Decoder
MUX accepts several inputs and allow only one data output.	It takes n input binary code and convert it into a corresponding outputs.
It can be used in data routing and waveform generation.	Application of decoder is in Decimal to BCD encoder.
Multiplexer converts the unary code into binary code	It converts binary code into unary..

Creating 5:1 MUX (multiplexer),  2:1 MUX will be required the Table and Diagram look like :

Table:

S2	S1	S0	Y
0	0	0	I0
0	0	0	I1
0	1	0	I2
0	1	1	I3
1	X	X	I4

Diagram

Karnaugh maps reduce logic functions more quickly and easily compared to Boolean algebra. By reduce we mean simplify, reducing the number of gates and inputs.So this cause we like to simplify logic to a lowest cost form to save costs by elimination of components. We define lowest cost as being the lowest number of gates with the lowest number of inputs per gate.

Multiplexer Look like in terms of K-map expression for basic 4:1 multiplexer  -

Y= Data Output D₀= Data input S₁,S₀ is selector then the expression is

Y= D₀S₁'S₀'+D₁S_1'S₀+D₂S₁S₀'+D₃S₁S₀

Assignment is Devloping circuit in lab. it is not posible to bulid it home .