Number System

Binary Number

Information is represented in logic circuits as electronic signals.

• Bit-wise operators
• Signed vs Unsigned Numbers

Converting Decimal to Binary

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.

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](https://www.scaler.com/topics/binary-subtraction/) for more details.

Subtraction With 2’s Complement

The idea is that $X-Y=X+(2^{\prime }\text{s complement of }Y)$ 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? $X-Y=X+(1^{\prime }\text{s complement of }Y)+\text{"carry"}$

Related

• Complement