Number System

Binary Number

Information is represented in logic circuits as electronic signals.

Converting Decimal to Binary

Screen Shot 2022-03-07 at 12.46.17 PM.png

Converting Binary to Decimal

Super simple, just add up all the numbers, multiplying 1 or 0 by the corresponding exponential value.

Binary Number Addition / Subtraction

I think this is pretty straightforward, just do the carry overs. Pasted image 20220417173409.png

For ECE124, they showed this technique called Substraction by addition.

title: Why am I learning this?
Sure, the above is easy to understand and do by hand, but computers can't do that. Instead, we thought of clever techniques to make arithmetic work. 
See this [article]( for more details.
Subtraction With 2’s Complement

The idea is that At the end of the addition,

  • If the final carry over of the sum is 1, it is dropped and the result is positive.
  • If there is no carry over, the two’s complement of the sum will be the result and it is negative
Subtraction with 1’s Complement

Basically same as 2s complement, a bit more confusing and fake?