Company LOGO DKT 1223 DIGITAL SYSTEM 1 E

Company LOGO DKT 122/3 DIGITAL SYSTEM 1 E d i t y o u r s l o g a n h e r e WEEK #9 FUNCTIONS OF COMBINATIONAL LOGIC (DECODERS & MUX EXPANSION)

Topic Outlines Company LOGO Encoder Ü Decoder Ü Multiplexers (MUX) Ü Demultiplexers (DEMUX) Ü

Topic Outlines Company LOGO Encoder Ü Decoder Ü Multiplexers (MUX) Ü Demultiplexers (DEMUX) Ü

Decoders Expansion Company LOGO Ü When a certain decoder size is needed, but only smaller number of sizes is available. Ü Combine 2 or more decoders in a hierarchy, i. e. cascade the smaller decoders to form a larger decoder size.

Decoder Expansion Company LOGO Example: A 3 -to-8 Decoder Constructed with Two 2 -to-4 Decoders

Decoder Expansion Company LOGO The Operation The MSB input, A 2, functions: – As enable, EN, of one decoder – As its complement, EN to the other decoder When A 2=0, – Top decoder enabled Generates minterms D 0 to D 3. – Lower decoder disabled Outputs equal to 0. When A 2=1, – Top decoder disabled Outputs equal to 0. – Lower decoder enabled Generates minterms D 4 to D 7.

Decoder Expansion Company LOGO The function of EN input Very useful and convenient way to interconnect 2 or more functional blocks Ü For the purpose of expanding digital functions into: Ü Similar functions with more inputs and outputs. Ü

Decoder Expansion Company LOGO Example: Implementing a Binary Adder Using a Decoder For an addition of X, Y, and Z (as Cin), the S and Cout expression are as follows: S(X, Y, Z) = m (1, 2, 4, 7) C(X, Y, Z) = m (3, 5, 6, 7) So, there are 3 inputs and 8 minterms Use a 3 -to-8 decoder.

Decoder Expansion Company LOGO Implementing a Binary Adder Using a Decoder - The logic circuit

Multiplexers (MUX) Company LOGO Ü MUX is a device that allows digital information from several sources to be routed onto a single line for transmission Ü It is made up of several datainput lines and a single output line. It also has data-select inputs which permits digital data on any one of the inputs to be switched to the output line. Ü MUX is also known as data selectors n select inputs 1 data output 2 n data inputs Logic symbol for a 4 -input multiplexer (4: 1 MUX)

Multiplexers (MUX) Company LOGO 2: 1 MUX Data selector SELECT input code determines which input is transmitted to output Z.

Multiplexers (MUX) Company LOGO 4: 1 MUX DATA-SELECT INPUTS 2 data-select lines means that any one of the 4 data-input lines can be selected D 0 D 1 D 2 D 0 D 1 D 3 S 1 4 -to-1 Z D 2 MUX S 0 S 1 S 0 Z INPUT SELECTED S 0 S 1 0 0 D 0 0 1 D 1 1 0 D 2 1 1 D 3 If a binary 0 (S 0=0 and S 1=0) is applied to the data-select lines, the data on input D 0 appear on the data-output line

Multiplexers (MUX) Company LOGO 4: 1 MUX Total expression for the data output is: Logic diagram for 4: 1 MUX

Multiplexers (MUX) Company LOGO Question 3 Construct an 8: 1 multiplexer using block diagram. 8 input lines means there must be 3 data select lines.

Multiplexers (MUX) Company LOGO Another design option for 8: 1 mux Ü Using construction of larger multiplexers from smaller ones. 16 -to-1 MUX: 74150

8 -to-1 -Line Multiplexer Company LOGO

16 -to-1 -Line Multiplexer Company LOGO

Multiplexers (MUX) Company LOGO Implementing a Boolean Function with a MUX A multiplexer is basically a decoder that includes the OR gate within the block. Ü To implement a Boolean function of n variables with a mux having n selection inputs and 2 n data inputs, one for each minterm. Ü The minterms are generated in a mux by the circuit associated with the selection inputs. Ü Individual minterms can be selected by the data inputs. Ü

Multiplexers (MUX) Company LOGO Implementing a Boolean Function with a MUX Ü Another method (more efficient way) Ü Implementing a Boolean function of n variables with a mux having only n-1 selection inputs and 2 n-1 data inputs.

Multiplexers (MUX) Company LOGO Implementing a Boolean Function with a MUX General procedure: 1. 2. 3. 4. 5. Produce Truth Table for Boolean function. The first n-1 variables are applied to the selection inputs of the mux. The remaining single variable of the function is used for the data input. For each combination of the selection variables, we evaluate the output as a function of the last variable, i. e. a 0, 1, the variable or its complement. These values are then applied to the data inputs in the proper order.

Multiplexers (MUX) Company LOGO Example Implement F (X, Y, Z) = m (1, 2, 6, 7) using 4: 1 MUX

Multiplexers (MUX) Company LOGO Example Implement F (A, B, C, D) = m (1, 3, 4, 11, 12, 13, 14, 15) using 8: 1 MUX

MUX Application Example Company LOGO 74157 - consists of four separate 2 -input multiplexers Content-selector Display

Demultiplexers (DEMUX) Company LOGO Ü DEMUX reverse the multiplexing functions Ü It takes digital information from one line and distributes it to a given number of output lines Ü DEMUX is also known as data distributor 1 data input 2 n data outputs n select inputs 1 -line to 4 -line DEMUX

Company LOGO Data input is transmitted to only one of the outputs as determined by the select input code. 1 -line-to-8 -line multiplexer

Demultiplexers (DEMUX) Company LOGO 1: 4 DEMUX The expression of every output

Demultiplexers (DEMUX) Company LOGO Question 4: Construct a 1: 4 DEMUX using block diagram. Show the equivalent Truth-Table. I 0 1 -4 DEMUX Q 0 Q 1 Q 2 Q 3 S 1 S 0 Block diagram S 1 S 0 I 0 Q 1 Q 2 Q 3 Logic circuit Truth-table S 1 S 0 I 1 Q 3 Q 2 Q 1 Q 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0

Mux-Demux Application: Example Company LOGO Ü This enables sharing a single communication line among a number of devices. Ü At any time, only one source and one destination can use the communication line.

Solve this. . Company LOGO Design the following: Ü Ü Ü 16 -line-to-4 -line encoder using the 8 -line -to-3 -line encoder in cascade A 4: 1 MUX using 2: 1 MUXes A 8: 1 MUX using 4: 1 MUXes A 1: 4 De. MUX using 1: 2 De. MUX A 1: 8 De. MUX using 1: 4 De. MUX E D N