Number Systems Journal 1

Examples of number systems

● Base 10 (Decimal) — Represent any number using 10 digits [0–9]

● Base 2 (Binary) — Represent any number using 2 digits [0–1]

● Base 8 (Octal) — Represent any number using 8 digits [0–7]

● Base 16(Hexadecimal) — Represent any number using 10 digits and 6 characters [0–9, A, B, C, D, E, F]

Base 10

"What about 24? In the case of two digits, the right digit says what it means, but the left digit means ten times what it says. That is, 4 is 4, 2 is 20. Altogether forms 24."

"If we take a three digit number, the right most digit means what it says, the middle one is ten times what it says, the left most digit 100 times what it says. Simply if we take number 546, it means 6 + (10 * 4) + (5 * 100) = 546."

Using this same logic taken from the reading and highlighted above 9873892848 for example breaks down as 8 + (10 * 4) + (1008) + (10002) + (100009) + (1000008) + (10000003) + (100000007) + (1000000008) + (10000000009) = 9873892848. As you can see the 0 acts as a placeholder within our base 10 decimal system.

Binary

Binary uses similar logic except it uses only two “values” 1 and 0. So in a binary system you continue to the right either with a 1 or a 0 value. For example, 0 followed by 1 then would be followed by 11 etc. 0 -> 1 -> 10 -> 11 -> 100 -> 101 - > 110 -> 111 -> 1000 -> 1001 -> 1110 -> 1111 -> 100000 -> etc.

When reading a binary number it is similar to any base 10 number. The value all the way to the right is its true value. Every number left of that represents 2^(n-2) assuming n represents the number of digits.

These rules and systems can apply to any different base number system. These systems are the base for encryption and encoding.

Hexadecimal

Hexadecimal uses numbers through 0-9 and A-F. A single value is represented by 4 binary digits. Hexadecimal values are not case sensitive and can be written with both uppercase and lowercase letters. Hexadecimal numbers can be translated into binary and vice versa using another number system like base 10. 52 in binary is 110100 (Found using the division method). 52 in hexadecimal is 34, I found this by dividing by 2 finding the remainder, and continuing the process until no coefficients existed. It is similar to the division method used in binary.

Signed/Unsigned numbers

The most significant bit used to represent negative numbers is 1. All negative numbers will have 1 as their most significant bit. Signed numbers can be negative or positive and anything in between however unsigned numbers can only be zero or positive.