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Binary Numbers

Binary numbers are very simple. In ancient Egypt and China, people coded some kind of logic using binary numbers. Leibniz saw in this the mystery of God: it is something from which the World is created from nothing -> something. Creatio ex nihilo (Latin for "creation out of nothing").

  • 0 - no light
  • 1 - there is light

God's binary

Binary/Boolean Logic​

Boole compiled truth table later. AND, OR, NOT etc.

Useful Counter​

This counter shows how to count in binary from numbers zero through thirty-one.

[0-3110]

Binary Numbers

Addition​

Addition is performed with carry. If 1 + 1.

  1 1  <- carry

   10101  = 21
+
    1110  = 14
  ------
  100011  = 35

Addition Table:

01
011
1110

Subtraction​

   0111 = 7
-
   1010 = 10
   ----
 1 1101  WTF?

Binary subtraction cannot subtract a large negative number from a small positive number (7-10)?????

You need to choose a different representation.

Subtraction with two's complement representation:

A - B = A + not B + 1

From: Binary Numbers (Wikipedia)