1. Chapter4: Combinational Logic Part 4 Originally By Reham S. Al-Majed Imam Muhammad Bin Saud University

2. Outline 2  Multiplexer  Definition  Examples  MUX and Decoder.  MUX Expansion.  Circuit Implementation with MUX  DeMultiplexer

3. Definition 3  It is a cc that select binary information from one of many input lines to single output line.  The selection of input line depends on selection lines.  Its ab consists of:  Inputs lines = 2 n  Output line = 1  Selectors (depends on number of inputs) = n  An active high or active low enable input (not all multiplexers have it) I 2 n -1 I0I0 MUX................ S0S0 S n-1 2 n Inputs lines n selection lines

4. Definition 4 I0I0 I1I1 I2I2 I3I3 00 MUX Y=I 0 I0I0 I1I1 I2I2 I3I3 10 MUX Y=I 1 I0I0 I1I1 I2I2 I3I3 01 MUX Y= I 2 I0I0 I1I1 I2I2 I3I3 11 MUX Y=I 3

5. Example 1 5  Design a 2-to-1 multiplexer: 1. 2 data inputs (I 0,I 1 ), 1 select input S, and 1 output (Y) 2. Truth table: SI1I1 I0I0 Y 000I0=0I0=0 001I0=1I0=1 010I0=0I0=0 011I0=1I0=1 100I1=0I1=0 101I1=0I1=0 110I1=1I1=1 111I1=1I1=1 SY 0 I0I0 1 I1I1

6. Example 1 (cont.) 6 3. Simplification: Y = S’ I 0 + S I 1 3. Diagram: 11 11 S I0I0 I1I1

7. Example 2 7  Design 4-to1 MUX:  There are four data inputs  two selection inputs S 1,S 0.  The input selected to be passed to the output depends on the minterm of the input. Y = S 1 ’S 0 ’I 0 + S 1 ’S 0 I 1 + S 1 S 0 ’I 2 + S 1 S 0 I 3 mintermS1S1 S0S0 Y m0m0 00 I0I0 m1m1 01 I1I1 m2m2 10 I2I2 m3m3 11 I3I3 m1m1 m2m2 m3m3 m0m0

8. Multiplexer and Decoder 8  The AND gates and inverters in the MUX resemble a decoder circuit.  They decode selection input lines.  2 n -to-1 line multiplexer is constructed from n-to-2 n decoder.  Example:  4-to-1 MUX constructed from 2-to-4 decoder

9. Multiplexer Expansion 9  Design a 4-to-1 MUX with 2-to-1 MUXes only.  4-to-1 has 4 data input, 2 selection input, and 1 output.  2-to-1 has 2 data input, 1 selection input, and 1 output. S1S1 S0S0 Y 00 D0D0 01 D1D1 10 D2D2 11 D3D3 D0D0 D1D1 MUX D2D2 D3D3 Y S0S0 S1S1 I0I0 I1I1 I0I0 I1I1 I0I0 I1I1

10. CC Implementation with MUX 10  Given a function of n-variables MUXex can be used to implement this function.  This can be accomplished in one of 2 ways:  Using a Mux with n-select inputs  n variables need to be connected to n select inputs.  Minterms of a function are generated according to select inputs.  Individual minterm can be selected by the data inputs  proper assignment of the data inputs (D i ∈ {0, 1}).  Using a Mux with n-1 select inputs (more efficient)  Find truth table.  The first n-1 variables in table are connected to selection inputs of MUX (which order ?).  For each combination of selection variables, evaluate output as function of the remaining variable (d)  This remaining variable (d) is then used for data inputs which can be 0,1,d,d’.

11. Example 1 11  Implement the function F(x,y,z) = ∑(1,2,6,7) using a Mux with n- select inputs.  The function has 3 variables  using 3-select inputs, we need a 8-to-1 MUX. 8-to-1 MUX x y z F 1 0 1 1 1 0 0 0 1 0 2 3 4 5 6 7

12. Example 2 12  Implement the function F(x,y,z) = ∑(1,2,6,7) using a Mux with n-1 -select inputs.  The function has 3 variables  using 2-select inputs, we need a 4-to-1 MUX. 4-to-1 MUX x y F z z’ 0 1 0 1 3 2

13. De-Multiplexer 13  It is a CC that performs the inverse operation of MUX.  It has:  1 input  2 n outputs.  n selection inputs to select outputs.  Example: design 1-to-4 DeMUX 1-to-4 DeMUX A1A1 E A0A0 D0D0 D1D1 D2D2 D3D3 A1A1 A0A0 D0D0 D1D1 D2D2 D3D3 00E000 010E00 1000E0 11000E

14. Reading 14  4.1  4.2  4.3  4.4  4.5  EXCEPT: Carry propagation.  4.6 Reading Assignment.  4.7 Reading Assignment.  4.9  4.10  4.11