Code Converter Digital Logic Lesson - Textbook

CHAPTER 7 CODE CONVERTER LESSON OUTCOMES  After complete this lesson, the students should be able to:  Understand the fundamentals of code conversion  Design and implement code conversion circuits  Differentiate between encoder and decoder  Differentiate between...

CHAPTER 7 CODE CONVERTER LESSON OUTCOMES  After complete this lesson, the students should be able to:  Understand the fundamentals of code conversion  Design and implement code conversion circuits  Differentiate between encoder and decoder  Differentiate between simple encoder and priority encoder  Construct the Boolean expressions using a decoder and OR gate CODE CONVERTER  A code converter is a combinational circuit that translates data from one type of binary code into another without altering the information's actual value. These circuits are widely used in digital systems to facilitate compatibility between different coding schemes or devices.  Code conversion :  performed by encoder, decoder and code converter circuits.  required to operate the electronic displays that show numbers or letters on calculators and clocks. CODE CONVERTER  E.g: the block diagram of calculator  The input device is a keyboard.  Between the keyboard and the CPU is an encoder - translates the decimal number pressed on the keyboard into a binary code such as BCD code.  The CPU performs its operation in binary and puts out a binary code.  The decoder translates the binary code from the CPU to a seven-segment display. ENCODER  Encoders are used in keyboard applications where activation of a single key must produce a unique binary code to represent its value.  Encoders have several inputs, but it converts only one input at a time into a binary code.  Encoders are usually specified by the number of inputs to outputs such as 4:2, 8:3 or 10:4 encoders. ENCODER  The job of the encoder in the calculator is to translate a decimal input to a BCD number.  A block diagram for a decimal-to-BCD or 10:4 encoder is shown below.  The encoder has 10 inputs on the left and 4 outputs on the right.  The encoder may have one active input and produces a unique output. ENCODER  The diagram show below is a truth table for a 10:4 encoder.  If decimal input 4 is activated, the output in BCD is 0100. ENCODER  The output expressions and the logic circuit : ENCODER  Example 1:  Design a 4:2 encoder, where only one input is active at any one time. Encoder  The 4:2 encoder truth table can be written in full as follows. The output expressions and the logic circuit: Exercises 1. The block diagram shown below is an 8:3 encoder: a) Derive the 8:3 encoder truth table b) Write the Boolean expression for the outputs c) Draw the logic circuit Solution: a) Truth table Input Output 0 1 2 3 4 5 6 7 A B C 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 b) Boolean expressions A=4+5+6+7 B=2+3+6+7 C=1+3+5+7 c) Logic circuit PRIORITY ENCODER  The simple 10:4 encoder identifies a drawback when more than one input is activated at one time – produced incorrect output for either activated input.  Priority encoder includes the necessary logic to ensure that when 2 or more inputs are activated, the output code will correspond to the highest numbered input.  E.g: when both 3 and 5 are activated, the output code will be 0101 (5). PRIORITY ENCODER  The 10:4 priority encoder with active-high inputs is shown below: PRIORITY ENCODER  As an example, suppose any of the input 0, 1 or 2 is activated, the output is a BCD 0010.  This is shown on the truth table as: 0 1 2 3 4 5 6 7 8 9 ABCD XX1 0 0 0 0 0 0 0 0 0 1 0 which represent : 0 1 2 3 4 5 6 7 8 9 A B C D 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 PRIORITY ENCODER  The output expressions can be written as:  This can be further simplified as: Priority Encoder  Example 2:  Design a 4:2 priority encoder:  From the truth table, the expressions can be written as : simplified -> Priority Encoder  The 4:2 priority encoder truth table can be written in full as follows: The expressions can be simplified using Karnaugh Map as: Exercises 1. The block diagram shown below is an 8:3 priority encoder: a) Derive the 8:3 priority encoder truth table b) Write the Boolean expression for the outputs c) Using Boolean algebra, simplify the expressions for A, B and C Solution: a) Truth table Input Output 0 1 2 3 4 5 6 7 A B C X 0 0 0 0 0 0 0 0 0 0 X 1 0 0 0 0 0 0 0 0 1 X X 1 0 0 0 0 0 0 1 0 X X X 1 0 0 0 0 0 1 1 X X X X 1 0 0 0 1 0 0 X X X X X 1 0 0 1 0 1 X X X X X X 1 0 1 1 0 X X X X X X X 1 1 1 1 b) Boolean expressions c) Simplified expressions: DECODER  A decoder - the opposite of an encoder.  A decoder translate from the BCD code to decimals.  The BCD codes form the input on the left of the decoder, and the output lines are on the right.  Only one output line will be activated at any one time.  A BCD 0011 input would activate the 3 output. DECODER  Example : 4:10 decoder DECODER  The output expressions and the logic circuit: DECODER  Example 1:  Design a 2:4 decoder.  A 2:4 decoder has 2 inputs and 4 outputs.  The output expressions and the logic circuit: Exercises 1. The block diagram shown below is an 3:8 decoder: a) Derive the 3:8 decoder truth table b) Write the Boolean expression for the outputs c) Draw the logic circuit Solution: a) Truth table Input Output A B C 0 1 2 3 4 5 6 7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 b) Boolean c) Logic circuit expressions DECODER APPLICATIONS  We can construct a Boolean expression using a decoder and logic gates.  A two variable Boolean expression for can be constructed using a 2:4 decoder and an OR gate. DECODER APPLICATIONS  A three variable Boolean expression can be constructed using a 3:8 decoder and an OR gate. Exercises 1. Draw the following expression using a decoder and an OR gate a) Solution: a) Solution: b) Solution: c) DISPLAY DECODER  A common output device used to display decimal numbers is the seven-segment display.  The seven-segments are labeled with standard letters from a to g.  For instance, if the segment a, b, c, d and g light, a decimal 3 appears. DISPLAY DECODER  The truth table for display decoder:  Test Yourself 1. Design a 4:2 priority encoder. 2. Design a 2:4 decoder. 3. Draw the following expressions using a decoder and an OR gate. a) Y A.B  B(A  C) b) Y A.B.C.D  A.B.C.D  A.B.C.D  A.D 10/9/2012 RA/Sept2012-Jan2013 38 END OF CHAPTER 7 CODE CONVERTER