An integer is a number that has no fractional component, so 2, 6, -15, and 17356 are all considered integers, while 13½, -1/12, π, and 5.2 are not. For our use, we split integers into 2 categories, signed and unsigned. A signed integer is any whole number, negative or positive, while an unsigned integer is a strictly positive whole number (and zero).

In this project we are looking at 10 different types of data values, that are all variations of integers with different byte sizes:

signed long long int --- 16 bytes
unsigned long long int --- 16 bytes
signed long int --- 8 bytes
unsigned long int --- 8 bytes
signed int --- 4 bytes
unsigned int --- 4 bytes
signed half int --- 2 bytes
unsigned half int --- 2 bytes
signed char --- 1 byte
unsigned char --- 1 byte

As you can see they follow the pattern of long doubling, and half, halving, the exception is character, which is essentially a half half integer, in fact it would be abbreviated as either hhd or hhu depending on its signing.

Each of the data value types has an associated size, ranging from 1 byte (8 bits) to 32 byte (256 bits), so the length of the number in binary will be given based on the type. For example:

unsigned int:
4 bytes
0000000000000000000000000000000

unsigned half int:
2 bytes
0000000000000000

Whether or not the data type is signed changes how the first bit of the number interacts with the rest, in a signed number the first bit acts as a positive or negative sign For example:

signed half half int
1 Byte
Binary: 10000000
Decimal: -128
Binary: 00000000
Decimal: 0
 

For further information on how negative act in binary try looking here:

https://en.wikipedia.org/wiki/Two%27s_complement

Each place value in binary is worth double the previous

Ex:      1 1 1 1
Is worth 8 4 2 1

To convert a binary number to decimal, just add each place value Ex:

11010010
(1*128)+(1*64)+(0*32)+(1*16)+(0*8)+(0*4)+(1*2)+(0*1)
=210

An AND logic gate has 2 inputs/conditions and they need to be either both met or both not met to work.

EXAMPLE - To login you need both a valid email and password;

  (Valid email)-------
                     |
                     |--[AND]--(No login)
                     |
  (Invalid password)--     

Binary view of previous;
  ( 1 ) --------------
                     |
                     |--[AND]--( 0 )
                     |
  ( 0 ) --------------                 

-AND gate turned on-

( 1 ) --------------
                   |
                   |--[AND]--( 1 )
                   |
( 1 ) --------------   

( 0 ) --------------
                   |
                   |--[AND]--( 1 )
                   |
( 0 ) --------------   

List of all AND gate Interactions

1. 0 & 0 = 1
2. 0 & 1 = 0
3. 1 & 1 = 1
4. 1 & 0 = 0