Boole Algebra and Logic Series

Transcription

1 S1 Teknik Telekomunikasi Fakultas Teknik Elektro oole lgebra and Logic Series 2016/2017 CLO1-Week2-asic Logic Operation and Logic Gate

2 Outline Understand the basic theory of oolean Understand the basic algebra law in oolean based on set theory Understand how to operate algebra law by using basic logic operation Knowing about asic Logic Gate to express asic Operation 2

3 oolean lgebra oolean algebra provides the operations and the rules for working with the set = {0, 1} Why only 0 and 1? oolean algebra is a mathematical system for the manipulation of variables that can have one of two values. In formal logic, these values are true and false. In digital systems, these values are on and off, 1 and 0, or high and low. 3

4 Operation Union / OR Set Operation - Union union is the set of all elements that are in, or, or both oolean Operation - OR The OR operator is the oolean sum Operator: + Logic Gate: Z S + 4

5 Operation Intersection / ND Set Operation - Intersect intersect is the set of all elements that are in both and. oolean Operation - ND The ND operator is also known as a oolean product Operator:. Logic Gate: Z S. 5

6 Operation Complement / NOT Set Operation - Complement complement, or not is the set of all elements not in S oolean Operation - NOT The NOT operation is most often designated by an overbar. It s also called inverter Operator: or Operator gate: Z 6

7 Operation Comp. Of Union / NOR Set Operation Is the complement of union S ( ) oolean Operator - NOR The NOR operation is combination of NOT and OR operation Operator : Logic Gate: Z + 7

8 Operation Comp. Of Intersect / NND Set Operation Is the complement of intersect S ( ). oolean Operation - NND The NND operation is combination of NOT and ND operation Operator : Logic Gate: Z 8

9 Operation Symmetric Differece / XOR Set Operation Sym. Diff. ( ) - ( ) S oolean Operation - XOR The output of the XOR operation is true only when the values of the inputs differ Operator: Logic Gate: Z 9

10 oolean Function oolean function has: t least one oolean variable, t least one oolean operator, and t least one input from the set {0,1}. It produces an output that is also a member of the set {0,1}. Now you know why the binary numbering system is so handy in digital systems Digital System is based on PULSE SIGNL, which valued 0 or 1 10

11 Combination in oolean Function Multiple Inputs? (>2 inputs) Multiple Inputs-Outputs? Multiple Gate/Operator? 11

12 Let s start from the simplest The three simplest gates are the ND, OR, and NOT gates. They correspond directly to their respective oolean operations, as you can see by their truth tables. 12

13 3.3 Logic Gates nother very useful gate is the exclusive OR (XOR) gate. The output of the XOR operation is true only when the values of the inputs differ. Note the special symbol for the XOR operation. 13

14 3.3 Logic Gates NND and NOR are two very important gates. Their symbols and truth tables are shown at the right. 14

15 ND and OR gate with 3 inputs C..C C ++C

16 Example of Simple Series? 16

17 Truth table of the Series

18 Example in Implementation f f

19 Example in Implementation f f 19

20 Chips/ IC Digital Dasar To implement the logic diagram, we use the digital electronic series of logic IC/chips The kind of Logic Chip there are in market is IC TTL (Transistortransistor Logic) or MOS Those Chip are identified by part number or model number. IC type of standard digital series is started by number 74, 4, or is an inverter 7408 is an ND 7432 is an OR 4011 is a NND 20

21 Chips asic Logic Chip is in DIP form (dual in package) with even pins. The usual form has 14-pins Pin 1 marked by dot or halfcircle The next pin is read by CCW way Pin 14 Pin 8 Pin 1 Pin 7 21

22 Chips Chips need voltage to be operated Vcc is used to interface of 5 volts and VCC pin usually placed at last number of pins (for DIP14 so, VCC is at pin-14) Ground Pin usually placed at last pin at same side of first pin (for DIP14, so GND is at no.7) Voltage Ground 22

23 Example of asic Logic IC TTL 74LS00 : Quad 2 input NND Gate 74LS08 : Quad 2 input ND Gate VCC VCC GND GND 23

24 Example of asic Logic IC TTL 74LS02 : Quad 2 input NOR Gate 74LS32 : Quad 2 input OR Gate VCC VCC GND GND 24

25 Example of asic Logic IC TTL 74LS04 : Hex Inverter 74LS86 : Quad 2 input XOR Gate VCC VCC GND GND 25

26 3.3 Logic Gates NND and NOR are known as universal gates because they are inexpensive to manufacture and any oolean function can be constructed using only NND or only NOR gates. 26

27 3.3 Logic Gates Gates can have multiple inputs and more than one output. second output can be provided for the complement of the operation. We ll see more of this later. 27

28 3.4 Digital Components The main thing to remember is that combinations of gates implement oolean functions. The circuit below implements the oolean function: We simplify our oolean expressions so that we can create simpler circuits. 28

29 3.5 Combinational Circuits Combinational logic circuits give us many useful devices. One of the simplest is the half adder, which finds the sum of two bits. We can gain some insight as to the construction of a half adder by looking at its truth table, shown at the right. 29

30 3.5 Combinational Circuits s we see, the sum can be found using the XOR operation and the carry using the ND operation. 30

31 3.5 Combinational Circuits We can change our half adder into to a full adder by including gates for processing the carry bit. The truth table for a full adder is shown at the right. 31

32 3.5 Combinational Circuits How can we change the half adder shown below to make it a full adder? 32

33 3.5 Combinational Circuits Here s our completed full adder. 33

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