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# IS 151 - Lecture 3

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IS 151 Lecture 3 - UDSM 2013

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### IS 151 - Lecture 3

1. 1. Basic Logic Operations • Basic Logic Operations – Several propositions combined form propositional/logic functions – Example: “The light is on” will be true if • “The bulb is not burned out” is true and if • “The switch is on” is true. – Logical statement: The light is on if and only if the bulb is not burned out and the switch is on – The first statement (the light is on – basic proposition) is true only if the last two statements (conditions) are true IS 151 Digital Circuitry 1
2. 2. Basic Logic Operations • Basic digital logic operations – NOT, AND, OR, Exclusive-OR IS 151 Digital Circuitry 2
3. 3. Basic Logic Operations – Features • Inputs – are on the left • Output – is on the right – A circuit that performs a specific logic operation is called a logic gate – The true/false conditions are represented by a HIGH (true) and a LOW (false) • HIGH = TRUE = 1 • LOW = FALSE = 0 IS 151 Digital Circuitry 3
4. 4. The NOT operation • Changes one logic level to the opposite logic level • When the input is HIGH, the output is LOW and vice versa • The NOT operation is implemented by a logic circuit called an inverter. IS 151 Digital Circuitry 4
5. 5. The AND operation • Produces a HIGH output if and only if all the inputs are HIGH • If one input is HIGH and the other is LOW, or all inputs are LOW, the output is LOW • The AND operation is implemented by a logic circuit called an AND gate. IS 151 Digital Circuitry 5
6. 6. The OR operation • Produces a HIGH output when any of the inputs is HIGH • Otherwise if all inputs are LOW then the output is LOW • The OR operation is implemented by a logic gate called an OR gate. IS 151 Digital Circuitry 6
7. 7. The Exclusive-OR operation • Produces a HIGH output when one and only one of the two inputs is HIGH • The Exclusive-OR operation is implemented by a logic gate called an EXOR gate. IS 151 Digital Circuitry 7
8. 8. Logic Operations - Review 1. When does the NOT operation produce a HIGH/LOW output? 2. When does the AND operation produce a HIGH/LOW output? 3. When does the OR operation produce a HIGH/LOW output? 4. When does the EX-OR operation produce a HIGH/LOW output? 5. What is an inverter? 6. What is a logic gate? 7. What is the difference between an OR and an Exclusive-OR operation? IS 151 Digital Circuitry 8
9. 9. Basic Logic Functions • The basic logic gates can be combined to form more complex logic circuits that perform many useful operations to build up complete digital systems • Some common logic functions: comparison, arithmetic, code conversion, encoding, decoding, data selection, storage, and counting IS 151 Digital Circuitry 9
10. 10. The Comparison Function • Magnitude comparison is performed by a logic circuit called the comparator. • A comparator compares two quantities and indicates whether or not they are equal. • Example: given two numbers, determine if the numbers are equal, and if not equal, which one is greater. IS 151 Digital Circuitry 10
11. 11. Arithmetic Functions • Addition – performed by an adder; adds two binary numbers (two inputs and a carry in) and generates an output and a carry out • Subtraction – performed by a subtracter; three inputs: two numbers and a borrow input; generates the difference and borrow out • Multiplication – performed by a multiplier; have two inputs, and an output (product) • Division – performed by a series of subtractions, comparisons and shifts; have two inputs and two outputs (quotient and reminder) IS 151 Digital Circuitry 11
12. 12. Code Functions • The Code conversion function – Changes a form of coded information into another coded form • The Encoding function – Converts information into some coded form • The Decoding function – Converts coded information into a nonencoded form IS 151 Digital Circuitry 12
13. 13. The Data Selection Functions • Multiplexer – switches digital data from several input lines onto a single output line in a specified time sequence • Demultiplexer – switches digital data from one input line to several output lines in a specified time sequence IS 151 Digital Circuitry 13
14. 14. Storage and Counting Functions • The Storage function – To retain binary data for a period of time; e.g. flip-flops, registers • The Counting function – To count events represented by changing levels or pulses or to generate particular code sequence. IS 151 Digital Circuitry 14
15. 15. • End of Lecture IS 151 Digital Circuitry 15