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 --- 8 bytes unsigned long long int --- 8 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
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
Hexadecimal Table:
0 1 2 3 4 5 6 7 8 9 A B C D E F
Hex |Binary |Decimal 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 A 1010 10 B 1011 11 C 1100 12 D 1101 13 E 1110 14 F 1111 15 ----------------------- 10 00010000 16 20 00100000 32 30 00110000 48 40 01000000 64 50 01010000 80 60 01100000 96 70 01110000 112 80 10000000 128 90 10010000 144 A0 10100000 160 B0 10110000 176 C0 11000000 192 D0 11010000 208 E0 11100000 224 F0 11110000 240 ------------------------- 11 00010001 17 12 00010010 18 13 00010011 19 14 00010100 20 15 00010101 21 16 00010110 22 17 00010111 23 18 00011000 24 ------------------------- FF 11111111 255 100 100000000 256
-Single digit-
5 + A = (5) + (10) Decimal = 15 Hexadecimal = F MAX SINGLE = F or 15 or 1111
-Double Digit-
1F + AB ((16*1)+15) + ((16*10)+11) Decimal = 31 + 171 = 202 Hexadecimal = CA MAX DOUBLE DIGIT = FF or 255 or 11111111
An AND logic gate has 2 inputs/conditions and they both need to be met to activate.
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 ) --------------
List of all AND gate Interactions
An OR logic gate has 2 input/conditions, that when one or both is met, the gate activates
EXAMPLE - You can have a free ice cream cone
(1scoopOfVanilla)---
|
|--[OR]--( free ice cream )
|
(0scoopsOfChocolate)
(1scoopOfVanilla)---
|
|--[OR]--( free ice cream )
|
(1scoopsOfChocolate)
(0scoopOfVanilla)---
|
|--[OR]--(No free ice cream )
|
(0scoopsOfChocolate)
List of all OR gate Interactions
An XOR logic gate has 2 input/conditions, that when one is met, the gate activates, cant be both
EXAMPLE - You can have a free ice cream cone, but you can only have one scoop of vanilla or chocolate
(1scoopOfVanilla)---
|
|--[XOR]--( free ice cream )
|
(0scoopsOfChocolate)
(0scoopOfVanilla)---
|
|--[XOR]--( free ice cream )
|
(1scoopsOfChocolate)
(0scoopOfVanilla)---
|
|--[XOR]--(No free ice cream )
|
(0scoopsOfChocolate)
(1scoopOfVanilla)---
|
|--[XOR]--(no free ice cream )
|
(1scoopsOfChocolate)
List of all XOR gate Interactions
A NOT gate inverts the input. It only has a single input.
EXAMPLE - Its opposite day
( YES )------|[NOT]>-----( NO ) ( 1 )--------|[NOT]>-----( 0 )
List of possible NOT gate interactions