研究室輪読で使用したスライド。 「コンピュータシステムの理論と実装」の1,2章。 This slide made for lab's group reading which treats "The Elements of Computer System".

1. 1
B3 shuya
The Elements of Computing System
- Ⅰ.Boolean Logic Ⅱ.Boolean Arithmetic -
B3 shuya

2. 2
Ⅰ. Boolean Logic

3. 3Introduction
Every digital device is composed by chips.
The component of chips is Logic Gate.
This chapter focus on Boolean Gate
which is simple and physically represent bool function.
This chapter implement boolean gate by using simulator.
I will show later how to use simulator.
3

4. 3Boolean Algebra 4
1.1.1 Boolean Algebra
Boolean algebra uses binary values.
This is labeled true/false, 0/1, yes/no, on/off.
The expresion of Bool function
Truth Table
Boolean expression
Canonical representation
Truth Table
f(x, y, z) = (x + y) · ¯z
Boolean expression
Canonical expression
f(x, y, z) = ¯xy¯z + x¯y¯z + xy¯z

5. Composite implementation of a three-way And gate
3Logic Gate 5
1.1.2 Logic gate
Gate is a physical device which implements function.
The simplest gates of all are made from tiny switching devices,
called transistors.
Primitive gate
Composite gate
This gate is combination of Primitive one.
This assembly called Logic design.

6. 6
Usage of Simulator

7. 3Usage of Simulator 7
Environmental construction
Download
http://www.nand2tetris.org/software/mac_guide.html
Setup
$ cd /usr/local/bin
$ ln -s ~/nand2tetris/tools/HardwareSimulator.sh HardwareSimulator
$ chmod +x HardwareSimulator
$ HardwareSimulator
Usage of Software
Click and load .hdl file. Click and load .tst file.
Run script

8. 8
Ⅱ. Boolean Arithmetic

9. 3Introduction
This chapter aims to make ALU.
All calculation on Computer executes by ALU.
The first section gives a brief Back-ground on
how binary codes and Boolean arithmetic can be used.
The Specification section describes a succession of
adder chips.
9

10. 3Usage of Simulator 10
Environmental construction
Download
http://www.nand2tetris.org/software/mac_guide.html
Setup
$ cd /usr/local/bin
$ ln -s ~/nand2tetris/tools/HardwareSimulator.sh HardwareSimulator
$ chmod +x HardwareSimulator
$ HardwareSimulator
Usage of Software
Click and load .hdl file. Click and load .tst file.
Run script

11. 3Boolean Arithmetic 11
Binary Numbers
Unlike the decimal system, which is founded on base 10,
the bi-nary system is founded on base.
Binary Addition
A pair of binary numbers can be added digit by digit from right to
left, the same method used in decimal addition.

12. 3Boolean Arithmetic 12
Signed Binary Numbers
The method used by almost all com-puters is called the
2’s complementmethod, also known asradix complement.
How to make 2’s complement
0101
1010
1011
Reverse bit order
1’s comlementmethod
add 1
2’s comlementmethod

13. 3Adders 13
half adder
This is designed to add two bits
sum = LSB of a + b,
carry = MSB of a + b
full adder
This is designed to add three bits
sum = LSB of a + b + c,
carry = MSB of a + b + c
adder
Designed to add two n-bit numbers
out = a + b

14. 3ALU 14
Arithmetic Logic Unit
ALU is component of PC. This executes boolean logic and arithmetic.
Previous gate is hold for any computer.
This section describes an ALU which is uniq one in this text.