Nand2 tetris 1and2
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The document discusses the fundamental components of computing systems, focusing on boolean logic, boolean arithmetic, and logic gates. It describes the implementation of boolean functions using a simulator and provides details on creating an arithmetic logic unit (ALU) for performing calculations in computers. Additionally, it explains the use of binary numbers and various types of adders in arithmetic operations.
Nand2 tetris 1and2
- 1. 1 B3 shuya The Elements of Computing System - Ⅰ.Boolean Logic Ⅱ.Boolean Arithmetic - B3 shuya
- 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.
- 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
- 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.