PowerPoint Overheads for

Computer ArchitectureFrom Microprocessors To Supercomputers

Behrooz Parhami

2

3

4

Figure 1.1 Some basic elements of digital logic circuits, with operator signs used in this book highlighted.

1.1 Signals, Logic Operator, and Gates

5

Figure 1.2 Gates with more than two inputs and/or with inverted signals at input or output.

6

Figure 1.3 An AND gate and a tristate buffer can act as controlled switches or valves. An inverting buffer is logically the same as a NOT gate.

7

Figure 1.4 Wired OR allows tying together of several controlled signals.

8

Figure 1.5 Arrays of logic gates represented by a single gate symbol.

9

1.2 Boolean Functions and Expressions

• Truth table– N-variable input: 2n

– x: don’t care. x in output column means no interest; x in input column means that function does not depend on the value of the particular variable involved.

• Logic expression– NOT takes precedence over AND– AND takes precedence over OR/XOR– Logic expression can be manipulated using laws of Boolean algebra in order to obtain an

equivalent logic expression for simpler or more suitable hardware realization.

• Word statement– Natural language

• Logic diagram– Graphical representation of a Boolean function that carries information about its

hardware realization.– Logic circuit synthesis: derive logic diagram from truth table, logic expression, or word

statement.– Logic circuit analysis: going backward from logic diagram to truth table, logic

expression, or word statement.

10

Table 1.1 Three 7-variable Boolean functions specified in a compact truth table with don’t-care entries in both input and output columns.

11

Table 1.2 Laws (basic identities) of Boolean algebra.

12

Figure 1.6 A two-level AND-OR circuit and two equivalent circuits.

1.3 Designing Gate Networks

13

Figure 1.7 Seven-segment display of decimal digits. The three open segments may be optionally used. The digit 1 can be displayed intwo ways, with the more common right-side version shown.

BCD to 7-segment decoder

14

x3x2x1x0 e0 e1 e2 e3 e4 e5 e6

0000 1

0001 0

0010 1

0011 1

0100 0

0101 1

0110 1

0111 0

1000 1

1001 0

012120201

0123012301230123012301233

xxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxe

15

Figure 1.8 The logic circuit that generates the enable signal for the lowermost segment (number 3) in a seven-segment display unit.

16

1.4 Useful Combinational Parts• Multiplexer

– 2a input signals: x0, x0, …,xN (N=2a-1) – Single output z– a control signal (address signal): y0, …, ya-1

• Decoder– a input signals– 2a output signals– Assert one and only one of its 2a output lines

• Encoder: opposite of a decoder.– 2a input signals– a output signals– When one and only one of its 2a input lines is asserted, its a-bit

output supplies the index of the asserted input in the form of a binary number

17

Figure 1.9 A multiplexer (mux), or selector, allows one of several inputs to be selected and routed to output depending on the binary value of a set of selection or address signals provided to it.

Multiplexer

Y z

0 x0

1 x1

18

Figure 1.10 A decoder allows the selection of one of 2a options using an a-bit address as input. A demultiplexer (demux) is a decoder that only selects an output if its enable signal is asserted.

Decodery1y0 X3 x2 x1 x0

00 0 0 0 1

01 0 0 1 0

10 0 1 0 0

11 1 0 0 0

19

Figure 1.11 A 2a-to-a encoder outputs an a-bit binary number equal to the index of the single 1 among its 2a inputs.

EncoderX3 x2 x1 x0 Active y1y0

0 0 0 1 1 00

0 0 1 0 1 01

0 1 0 0 1 10

1 0 0 0 1 11

0 0 0 0 0 xx

20

Figure 1.12 Programmable connections and their use in a PROM.

Programmable Combinational Parts

21

Figure 1.13 Programmable combinational logic: general structure and two classes known as PAL and PLA devices. Not shown is PROM with fixed AND array (a decoder) and programmable OR array.

22

PLD: Short for programmable logic device, a generic term for an integrated circuit that can be programmed in a laboratory to perform complex functions.

(i) PROMs (Programmable Read Only Memory) - offer high speed and low cost for relatively small designs (ii) PLAs (Programmable Logic Array) - offer flexible features for more complex designs (iii) PAL/GALs (Programmable Array Logic/Generic Array Logic) - offer good flexibility and are faster and less expensive than PLAs

23

Figure 1.14 Timing diagram for a circuit that exhibits glitching.

Example: f = x + y + z, using circuit in Fig.13b

24

CMOS: Complementary metal–oxide–semiconductor

25

A (Vin )

C B (Vout )

The CMOS transmission gate

P

N

s

s

MOS Circuit TG Symbol

The conduction path through TG is controlled bycomplementary signals & ss

A(Vin) S Tn Tp B (Vout)0 0 off off Z (high impedance state (blocks logic flow))

0 1 on off 0 (nMOS passes strong 0, pMOS off when Vout<Vthp)

1 0 off off Z (high impedance state (blocks logic flow))

1 1 off on 1 (pMOS passes strong 1, nMOS off when Vout>Vdd-Vthn )

B (Vout )

s

s

A (Vin )

B=A(or Z when S=0)

s

s

A In steady state