1. Logic Design Computer Architecture and Design Lecture 1

2. Youpyo Hong & Kangwoo Lee @ DGU Computer Architecture? Instruction set  operation encoding, memory addressing techniques Data representations  signed magnitude, floating-point Addressing  direct, indirect, relative I/O mechanisms  memory mapped, I/O mapped So, it is a mixture of hardwares and softwares. 2

3. Youpyo Hong & Kangwoo Lee @ DGU HW & SW for Computers Hardware : Electronic components & electromechanical devices that comprise the physical entity of the device Software : Programs composed of a sequence of instructions  System Software Programs to make use of the core function of computers Example: Operating systems, Compilers  Application Software Programs for various users application Example: Games, Word-processor  Firmware Programs directly related to hardware control Example: Device driver 3

4. Youpyo Hong & Kangwoo Lee @ DGU Computer Hardware We have learned hardware design in digital logic design courses. Brief review on digital logic design follows. 4 Memory Central processing Unit Central processing Unit Input-Output processor Input-Output processor Input devices Input devices Output devices Output devices

5. Youpyo Hong & Kangwoo Lee @ DGU Transistors : Basic Elements for HW Logic gates are physically implemented by Transistors. If N & P transistors in a single semiconductor place, it is called CMOS technology. 5 N - type V CA nS C B A - + P - type V BC pS C B A - + Source Drain Gate C B A C B A Source Drain Gate C B A C B A Switch Transistor Logic Symbol

6. Youpyo Hong & Kangwoo Lee @ DGU v out C B A C B A V DD v in xz Details on transistors are covered in semiconductor & integrated circuit design courses. Our design ground is digital logic as follows. Inverter Gate 6

7. Youpyo Hong & Kangwoo Lee @ DGU Boolean Algebra Boolean algebra is an algebra that deals with binary variables and logic operations. Three representations for a function.  Boolean Function ( = Logic Expression) Algebraic expression with binary variables, logic operation symbols, parenthesis & equal sign  Truth Table A relationship between the function and its variables  Logic Diagram Expression of Boolean function using logic gates 7

8. Youpyo Hong & Kangwoo Lee @ DGU Examples 8  Truth Table x y z F  Logic Diagram x y z 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 F F = x + y’z  Boolean Function

9. Youpyo Hong & Kangwoo Lee @ DGU Logic Simplification Why ?  To minimize the number of logic gates, the propagation delay and the cost while performing the same function How?  Using the basic identities of Boolean algebra or  Using the karnaugh-map simplification or  Using other approaches 9

10. Youpyo Hong & Kangwoo Lee @ DGU Karnaugh-Map Simplification 10 11 1 1 11 1 0001 11 10 00 01 11 AB CD F(A,B,C,D) =  (0,1,2,6,8,9,10) F = BD’ + B’C’ + A’CD’ 1 1 11 10 1 0 000111 A BC F(A,B,C) =  (3,4,6,7) F = BC + AC’ 1 11 1 1 10 1 0 000111 A BC F(A,B,C) =  (0,2,4,5,6) F = C’ + AB’

11. Youpyo Hong & Kangwoo Lee @ DGU Combinational Logic (= Circuit) Outputs are determined by current inputs only. (No memory in combinational logic.) 11 Combinational Circuit m output variables n input variables  Problem statement  Assign letter symbols to I/O  Build a truth table  Simplification for each output  Logic Diagram Circuit Design Procedure

12. Youpyo Hong & Kangwoo Lee @ DGU Half Adder Example 12 xy 00 CS 00 01 10 01 01 1110 Truth Table S = x’y + xy’ = x  y C = xy Boolean Function x y C S Logic Diagram

13. Youpyo Hong & Kangwoo Lee @ DGU Sequential Logic Outputs are determined by current inputs and the memory contents. Basic unit of memory is flip-flop that stores 1 bit information. You need to understand the concept of latch, register and RAM. 13

14. Youpyo Hong & Kangwoo Lee @ DGU Flip-Flops 14 Q(t)Q(t+1) 00 SR 0x 01 10 10 01 11x0 SR Flip-Flop Q(t)Q(t+1) 00 D 0 01 10 1 0 111 D Flip-Flop Q(t)Q(t+1) 00 JK 0x 01 10 1x x1 11x0 JK Flip-Flop Q(t)Q(t+1) 00 D 0 01 10 1 1 110 T Flip-Flop

15. Youpyo Hong & Kangwoo Lee @ DGU Sequential Circuit Configuration 15 Combinational Circuit inputsoutputs Flip-Flops clock

16. Youpyo Hong & Kangwoo Lee @ DGU Sequential Circuit Design Flow 16  Draw a State Transition Diagram  Assign state Variables to the states  Determine the types of flip-flops to use  Translate state diagram to State Table with current states, inputs, outputs, next states  Extend state table to Excitation Table including inputs to flip-flops  Determine Boolean functions for the outputs and for the inputs of flip-flops  Draw a Logic Diagram

17. Youpyo Hong & Kangwoo Lee @ DGU Sequential Circuit Example 17 J Q K J Q K A B clock x J A = BxJ B = x K B = xK A = Bx  State Diagram  Variables  Flip-flop types  State Table  Excitation Table  Boolean function  Logic Diagram Procedure