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컴퓨터구조론 교수 채수환

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교재 Computer Systems Organization & Architecture John D. Carpinelli, 2001, Addison Wesley

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평가방법 중간고사 40% 학기말 고사 40% 레포트 및 출석 20% 계 100% 단 결석 ¼ 이상은 F 학점

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What must you do as a junior student Improve your grade up to at least 3.5/4.5. Cultivate your English ability. Make good relationship with your friends. Think your future seriously. Be an expert in your field. Be flexible.

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Chapter 1 Digital Logic Fundamentals Boolean Algebra Basic Combinatorial Logic More Complex Combinatorial Components Combinatorial Circuit Design Basic Sequential Components More Complex Sequential Components Real World Example: PLD

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1.1 Boolean Algebra Basic Functions AND NAND OR NOR NOT XOR XNOR (or Equivalence) Table 1.3: All possible binary Boolean functions

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1.1 Boolean Algebra( 계속 ) Manipulation of Boolean Algebra DeMorgan ’ s Law Minterm Karnaugh map(K-map)

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1.1 Boolean Algebra( 계속 ) DeMorgan ’ s Law It allows a digital designer to convert an AND function to an equivalent OR function and vice versa. (ab) ’ =a ’ +b ’ (a+b) ’ =a ’ b ’ Example: (xy ’ +yz) ’ =(xy ’ ) ’ (yz) ’ =(x ’ +y)(y ’ +z ’ ) =x ’ y ’ +x ’ z ’ +yy ’ + yz ’ = x ’ y ’ +x ’ z ’ + yz ’

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1.1 Boolean Algebra( 계속 ) Minterm Each possible AND set of input values If there are two input values, x and y, there are four possible minterms: x ’ y ’, x ’ y, xy ’, xy

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1.1 Boolean Algebra( 계속 ) K-map (Karnaugh-map) A useful device for minimizing logic

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Figure 1.1 K-maps

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1.1 Boolean Algebra( 계속 ) K-map The ordering of K-map inputs: Gray code A Gray code is a reflected code.

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Figure 1.2 Gray code sequence generation

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1.1 Boolean Algebra( 계속 ) Grouping on K-map Prime Implicants(PI) Essential Prime Implicants(EPI): groups which include cells that covered by only one group.

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Figure 1.3 (xy’+yz)’

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Figure 1.4 More complex function

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1.1 Boolean Algebra( 계속 ) Don ’ t care When some patterns of input values will never occur, it is called don ’ t care condition. We can treat the don ’ t care values as either 0 or 1, whichever makes it easier to group the minterms.

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Figure 1.5 A 7-segment LED driver

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1.2 Basic Combinatorial Logic Gates: digital components that implement the logic functions. AND OR NOR NOT NAND NOR XNOR

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Figure 1.6 Logic Symbols

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1.2 Basic Combinatorial Logic(continued) The gates can be combined to realize more complex functions. There are some realization ways for a given complex functions depending on the conditions.

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Figure 1.7 Two realization of the function wx’+x’z’+w’xyz

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1.2 Basic Combinatorial Logic(continued) Buffers: Buffers do not perform any operations on its input. Regular buffer: to boost the current of input to a higher level Tri-state buffer: it has a data input, just like the regular buffer, but also an enable input, E. If E is disable state, it produces a high impedance output.

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Figure 1.8 Logic symbols for buffers Buffers: Regular buffers(simply buffers): for boosting the current Tri-state buffers: enable, high-impedance

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1.3 More Complex Combinatorial Components Multiplexer(MUX) It chooses one of its data inputs and passes it through to its output. Select signals are needed for select a data input

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Figure 1.9 (a) Internal configuration of 4-to-1 MUX

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Figure 1.9 (b) Schematic representation with an active high enable signals

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Figure 1.9 (c) Schematic representation with an active low enable signals

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Figure 1.10 A 4-to-1 MUX constructed using 2-to-1 MUXs

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1.3 More Complex Combinatorial Components(continued) Decoder It accepts a value and decodes it. It has n inputs and 2 n outputs, numbered from 0 to 2 n – 1.

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Figure 1.11 Internal Configuration of a 2-to-4 decoder

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Figure 1.11 (b) Schematic representation with an active high enable signals

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Page 19, Figure 1.11 (c) Schematic representation with an active low enable signals

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1.3 More Complex Combinatorial Components(continued) Encoder It is the exact opposite of the decoder. It receives 2 n inputs and outputs an n-bit value corresponding to the input value.

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Figure 1.12 (a) Internal Configuration of a 4- to-2 encoder

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Figure 1.12 (b) Schematic representation with an active high enable signals

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Figure 1.12 (c) Schematic representation with an active low enable signals

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1.3 More Complex Combinatorial Components(continued) Priority encoder The encoder works if zero or one inputs are active, but fails. A priority encoder works just like a regular encoder, with one exception, Whenever more than one input is active, the output is set to corresponding to the highest active input.

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Figure 1.13 (a) A 4-to-2 priority encoder

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Figure 1.13 (b) and (c) The other 4-to-2 priority encoder and its truth table

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1.3 More Complex Combinatorial Components(continued) Comparator It compares two n-bit binary values to determine which is greater, or if they are equal.

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Figure 1.14 1-bit comparator

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Figure 1.15 1-bit comparator with propagated inputs

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Figure 1.16 n-bit comparator constructed using 1-bit comparators with propagated inputs

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1.3 More Complex Combinatorial Components(continued) Adder Adders are most commonly used, not only to perform addition, but also to perform subtraction, multiplication, and division. Half adder Full adder Ripple adder Carry lookahead addeer

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Figure 1.17 A half adder

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Figure 1.18 a full adder

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Figure 1.19 4-bit adder constructed using full adders

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1.3 More Complex Combinatorial Components(continued) Full subtracter A full subtracter(Figure 1.20) Two ’ s complement addition By doing this, a CPU may use a parallel adder for addition and subtraction.

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Figure 1.20 A full subtracter

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1.3 More Complex Combinatorial Components( 계속 ) Memory It is a group of circuit used to store data. Address inputs Data lines Classes of memory chips depending on volatility ROM RAM

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Figure 1.21 ROM and RAM

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1.4 Combinatorial Circuit Design BCD to 7-Segment Decoder

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Figure 1.22 A 7-Segment LED display

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Figure 1.23 (a) K-maps for designing segments

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Figure 1.23 (b) Circuits to implement segments b and c

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Figure 1A : LEDS (a) active high (b) active low

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1.4 Combinatorial Circuit Design(continued) A sorter

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Figure 1.24 (a) A two-input compare- and –swap module

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Figure 1.24 (b) four-input data sorter

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1.5 Basic Sequential Components The most fundamental components are latch and flip-flop Latch: level-triggered Flip-Flop: edge-triggered Triggering Positive Negative Clock It is used to synchronize the flow of data in a digital system

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Figure 1.25 clock sequence

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1.5 Basic Sequential Components(continued) D latch and D F-F It has one input, D, and a clock input. The value of D becomes output, Q, after some delay. LD signal: It must be high as the clock changes from 0 to 1 in order for the data to be loaded into the F-F.

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Figure 1.26 (a) Positive-edge triggered D F-F

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Figure 1.26 (b) Positive-level triggered D latch

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Figure 1.27 Positive level triggered D latch with set and clear

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Figure 1.28 SR latch

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1.5 Basic Sequential Components(continued) JK-FF It resolves the problem of undefined when SR=11

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Figure 1.29 J-K F-F

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Figure 1.30 T F-F

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1.5 Basic Sequential Components(continued) Flip-flops and latches may be combined in parallel to store data with more than one bit.

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Figure 1.31 4-bit D F-F

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1.6 More Complex Sequential Components Counters It stores a binary value and, when signaled to do so, arithmetically increases or decreases its value. Ripple counter Up/down counter

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Figure 1.32 4-bit Counter

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Figure 1.33 4-bit up/down counter

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1.6 More Complex Sequential Components Shift registers it can shift data one bit position to the right or left. It is particularly useful for certain hardware multipliers and dividers.

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Figure 1.34 4-bit left-shift register

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1.7 Real World Example PLA PAL PLD FPGA

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Figure 1.35 PLA programmed b=x2’+x1’x0’+x1x0 and c=X2+X1’+X0

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Figure 1.36 PAL programmed b=x2’+x1’x0’+x1x0 and c=X2+X1’+X0

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