EECE312_Ch_03_Digital

# EECE312_Ch_03_Digital - EECE312 Electronics Dr. Walid...

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Chapter 3: Digital Logic Circuits EECE312 Electronics Dr. Walid Kamali Fall 2007 1

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Objectives Discuss the essential features of digital logic circuits Presenting an introduction to combinational logic circuits Understand the concepts of analog signals and digital signals, Convert between decimal and binary numbers and use the hexadecimal system and BCD and Gray codes Write truth tables and realize logic functions Design logic functions using Karnaugh maps Study various combinational logic modules, including multiplexers, memory and decoder elements, and programmable logic arrays. 2
Analog and Digital Signals Analog signal : An analog signal is an electric signal whose value varies in analogy with a physical quantity such as: Time, temperature, force, acceleration,… Example: An analog function of time f (t) ,for each value of time, f (t) can take only one value among any of the values in a given range. 3

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Analog Voltage of Internal Combustion Engine in- Cylinder Pressure 4
Digital Signal A digital signal: A digital signal is a signal that can take only a finite number of values. Example: A signal that allows the display of a temperature measurement on a digital readout. The display will read 0 if the sensor voltages are between 0 and 49 mv and 1 if the sensor voltages are between 50 and 100 mv. 5

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Binary Signal Binary signal: A binary signal is a signal can take only one of two discrete values and is therefore characterized by transitions between two states. 0-1; 0V,5V (TTL convention) The transitions are called edges and can be Positive( f 0 to f 1 ) or Negative ( f 1 to f 0 ) 6
Number System A number is represented by a string of digits. Each digit has an associated weight Number = weighted sum of digits Example 1 : 534 = 5x100 + 3x10 + 4x1. The weights are power of 10: 100, 10, 1 Example 2 : 85.28 = 8x10 + 5x1 + 2x0.1 + 8x0.01 -We have positive and negative powers -This system had a base (radix, r) of 10 7

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The binary number system is used to represent one of two states: ON, OFF; (0,1) Used to represent numbers in a digital system Example : 10110 2 = 1x2 4 +0x2 3 +1x2 2 +1x2 1 +0x2 0 =22 10 Example: 110.01 = 1x2 2 +1x2 1 +0x2 0 +0x2 -1 + 1x2 -2 = 6.25 10 bit (binary digit): The smallest unit of information handled by a computer. One bit expresses a 1 or a 0 in a binary numeral Least significant bit, LSB : the rightmost bit Most significant bit, MSB : the leftmost bit Nibble : group of 4 bits Byte: group of 8 bits Word : group of 16 bits or 2 bytes. Binary: radix = 2 8
Addition and Subtraction 0+0=0 0-0=0 0+1=1 1-0=1 1+0=1 1-1=0 1+1=0 (with a carry of 1) 0-1=1 (with a borrow of 1) A carry is generated whenever the sum of two digits exceeds the largest single-digit number in the given number system, which is 1 in the binary system 9

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Examples 5 6 11 + 101 110 1011 + 16 3 13 - 10000 11 01101 - 10
Multiplication and Division In the decimal system the multiplication table

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## This note was uploaded on 02/07/2011 for the course EECE 312 taught by Professor Walidkamali during the Fall '07 term at American University of Beirut.

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EECE312_Ch_03_Digital - EECE312 Electronics Dr. Walid...

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