CHAPTER 2 Digital Combinational Logic/Arithmetic Circuits

 Converters  Converters - Comparator - Decoder - Encoder - Code Converter

Comparator(1)  Compares two binary strings (or binary words) to determine if they are exactly equal.  Truth table for a comparator: A BA=B

 E.g. to design a comparator to evaluate two 4 bit numbers, we need 4 Ex-NORs and a 4 input AND gates  8 bit magnitude comparator: Comparator(2)

Encoder(1)  Encoder converts information such as decimal number or an alphabetical character into some binary coded form.  Encoder is usually used for:  Data representation  Data security  Data compression

Example: 8-to-3 Binary Encoder Encoder(2) 0

Design a Decimal-to-BCD Encoder: 1. Comes out with a truth table (input/output) 2. From a truth table, get the equation for each output 3. Draw a circuit for basic decimal-to-BCD encoder based on output equation. Note : Do not forgot to label LSB & MSB Encoder(3)

 A decoder is a circuit that creates an output based on the binary states of a given input Decoder(1)

 In digital electronics, a decoder can take the form of a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs, where the input and output codes are different. e.g. n-to- 2 n BCD decoders.  Enable inputs must be ON for the decoder to function, otherwise its outputs assume a single "disabled" output code word. Decoding is necessary in applications such as data multiplexing, 7 segment display and memory address decoding. Decoder(2)

Example: 3 to 8 Binary Decoder Decoder(3)

Decoder(4)

Example: 7 Segment Decoder  A 7 segment decoder has 4-bit BCD input and the seven segment display code as its output.  In minimizing the circuits for the segment outputs all non-decimal input combinations (1010, 1011, 1100,1101, 1110, 1111) are taken as don’t-cares ( X ) /Bl D C B A a b c d e f g 0 x x x x don’t care inputs -- Decoder(5)

 Example: Application Decoder(6)

 Device that converts one type of binary representation to another.  Example : BCD to binary and binary to Gray code.  Binary code vs. Gray Code. To convert binary to Gray code or Gray code to binary, we use X-OR gates. How??? Code Converter(1)

 Also known as Data selector.  SELECT input code determines which input is transmitted to output Z. A 2 input multiplexer Multiplexer(1)

 A multiplexer or MUX is a device that selects one of several analog or digital input signals and forwards the selected input into a single line. A multiplexer of 2 n inputs has n select lines, which are used to select which input line to send to the output.  An electronic multiplexer makes it possible for several signals to share one device or resource.  E.g: one ADC or one communication line, instead of having one device per input signal. Multiplexer(2)

A 4 input multiplexer Multiplexer(3)

 Larger multiplexers can be constructed from smaller ones.  An 8-to-1 multiplexer can be constructed from smaller multiplexers as shown: Multiplexer(4)

 Example: Application Multiplexer(5)

 Data input is transmitted to only one of the outputs as determined by select input code 1-line-to-8-line multiplexer Demultiplexer(1)

Demultiplexer(2)  A demultiplexer (or DEMUX) is a device taking a single input signal and selecting one of many data- output-lines, which is connected to the single input.  A multiplexer is often used with a complementary demultiplexer on the receiving end.  An electronic multiplexer can be considered as a multiple-input, single-output switch, and a demultiplexer as a single-input, multiple-output switch.

 Example: 1- to -4 Demultiplexer Demultiplexer(3)

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