Elements of Computing Systems Chapter 2

Notes from London Computation Club's second NAND2TETRIS meeting from Mon 24th Nov, covering chapter 2

Preamble

• Decided not to review chap 1
• Most had read chap 2
• Half had completed/attempted the exercises

2’s Complement

• Number line
• Get from positive to negative by flipping all the bits and adding 1
• Think about odometers
• Easy to map positive to negative
• Easy to add negative to positive
• Almost all computers use it… which don’t?
• How Ruby encodes negative integers

Half adder

• Obfuscation of LSB/MSB
• Seemed obvious enough from the truth table
• Drew on the whiteboard

Full adder

• Drew on the whiteboard
• Start by half-adding a and b
• Then half-add sum1 and c
• We throw away the overflow, why is that okay?
• Is there a way to do it without half-adders?
• Worked through the canonical form HOMEWORK

Add16

• Fundamentally about chaining the carry bit through
• No overflow

ALU

• Why is this interesting?
• Provides a selection of useful functions and some other stuff we don’t care about
• Do we need x+1 and x-1? Depends on the architecture?
• Decompose the operations into crafty ways to perform the operations we’re after
• Tried to reason through some of the operations
• 2’s complement relied upon
• Our completed ALU

Other Notes

• Increase frequency of meetups?
• 3 weeks for the next 2, then talk about it again
• James’ rake command to avoid the GUI
• Chris: look into other ideas of how to design an ALU
• James’ real life version with Arduino
• Could we buy these chips off the shelf and build the real thing?