Honors ICS - 1 : Bit Operations

Logic is about “Proof”

1. Every step must be very solid and accurate
2. Coherent

Bit Operations

3 basic operations (gate):

• AND
• OR
• NOT

Voltage -> Bit

Problem : Addition (Summation)

We will start at 1-bit addition like 1-digit addition

If will do not consider the carry out, but only the carry in. $C=1$ is one iff $A\neq B$

A\oplus B=(A\and \neg B)\or(\neg A\and B)

To simplify, we use a box:

Therefore, $\overline{S_nS_{n-1}\dots S_1S_0}=A+B$

Major Challenge : speed (Need to be count step by step)