Boolean Logic. Building a Modern Computer From First Principles.

Transcription

1 Boolen Logic Building Modern Computer From First Principles Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 1

2 Usge nd Copyright Notice: Copyright Nom Nisn nd Shimon Schocken This presenttion ccompnies the textook The Elements of Computing Systems y Nom Nisn & Shimon Schocken, MIT Press, We provide 13 such presenttions. Ech presenttion is designed to support 3 hours of clssroom or self-study instruction. You re welcome to use or edit this presenttion s you see fit for instructionl nd noncommercil purposes. If you use our ook nd course mterils, plese include reference to If you hve ny questions or comments, plese write us t nnd2tetris@gmil.com This work is licensed under Cretive Commons Attriution-NonCommercil-ShreAlike 3.0 Unported License. Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 2

3 Boolen lger Some elementry Boolen functions: Not(x) And(x,y) Or(x,y) Nnd(x,y) Boolen functions: x y z f ( x, y, z) = ( x + y) z x Not(x) x y Or(x,y) x y And(x,y) x y Nnd(x,y) A Boolen function cn e expressed using functionl expression or truth tle expression Importnt oservtion: Every Boolen function cn e expressed using And, Or, Not. Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 3

4 Boolen lger Given: Nnd(,), flse We cn uild: Not() = Nnd(,) true = Not(flse) And(,) = Not(Nnd(,)) George Boole, ( A Clculus of Logic ) Or(,) = Not(And(Not(),Not())) Xor(,) = Or(And(,Not()),And(Not(),))) Etc. Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 4

5 Multiplexer sel Mux sel sel 0 1 Proposed Implementtion: sed on Not, And, Or gtes. Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 5

6 Exmple: Building n And gte And.cmp Contrct: And When running your.hdl on our.tst, your. should e the sme s our.cmp. And.hdl And.tst CHIP And { IN, ; OUT ; // implementtion missing } lod And.hdl, put-file And., compre-to And.cmp, put-list ; set 0,set 0,evl,put; set 0,set 1,evl,put; set 1,set 0,evl,put; set 1, set 1, evl, put; Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 6

7 Building n And gte Interfce: And(,) = 1 exctly when ==1 And And.hdl CHIP And { IN, ; OUT ; // implementtion missing } Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 7

8 Building n And gte Implementtion: And(,) = Not(Nnd(,)) And.hdl CHIP And { IN, ; OUT ; // implementtion missing } Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 8

9 Building n And gte Implementtion: And(,) = Not(Nnd(,)) Nnd x in Not And.hdl CHIP And { IN, ; OUT ; // implementtion missing } Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 9

10 Building n And gte Implementtion: And(,) = Not(Nnd(,)) NAND x in NOT And.hdl CHIP And { IN, ; } OUT ; Nnd( =, =, = x); Not(in = x, = ) Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 10

11 Hrdwre simultor (demonstrting Xor gte construction) HDL progrm test script Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 11

12 Hrdwre simultor HDL progrm Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 12

13 Hrdwre simultor HDL progrm put file Elements of Computing Systems, Nisn & Schocken, MIT Press, Chpter 1: Boolen Logic slide 13