Binary

From Computer Science Wiki
This is a basic concept in computer science

In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.[1]


Binary[edit]

This is one of the better videos I've seen on binary. Content gratefully used with permission : [2]


Basic Definitions[edit]

  • bit: A binary digit, either a 0 or 1.
  • byte: A group of 8 adjacent binary digits (8 bits), on which a computer operates as a unit
  • binary: The binary numeral system is a base 2 number system.
  • denary/decimal: The decimal numeral system (also called base 10 or occasionally denary) has ten as its base.[3]
  • hexadecimal: In mathematics and computing, hexadecimal (also base 16, or hex) is a positional numeral system with a radix, or base, of 16[4]. Click here for an excellent video about hexidecimal

Binary translation table[edit]

I find it helpful to draw this table when I must convert binary to base 10. It also helps when looking at the video above.

128 64 32 16 8 4 2 1

A helpful cheat sheet[edit]


NumberSystems.png


How to add two binary numbers[edit]

Adding binary is straight forward. Line up the numbers as you would if you were adding base-10 numbers.

Remember this:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10, so write a 0 and carry the 1 to the next column.

What you must know[edit]

You must be able to correctly answer the following questions:

  • Define the term: bit
  • Define the term: byte
  • Define the term: binary
  • Define the term: denary/decimal (they refer to the same thing)
  • Define the term: hexadecimal

Why is this so important?[edit]

If we can represent numbers as 1 and 0, why not represent numbers as on and off? If we can represent letters as numbers (A = 65, B = 66) couldn't we also say A = 01000001 and B = 01000010? We can follow this line of thinking and make north / south, up / down, and low / high. Simple constructions that we can use to represent more complex numbers and even letters.

Binary representation is the essence of how computers work.

Resources[edit]

Click here for a slide deck that covers this topic nicely

References[edit]

A unit of abstract mathematical system subject to the laws of arithmetic.

Represent by means of a labelled, accurate diagram or graph, using a pencil. A ruler (straight edge) should be used for straight lines. Diagrams should be drawn to scale. Graphs should have points correctly plotted (if appropriate) and joined in a straight line or smooth curve.

Give the precise meaning of a word, phrase, concept or physical quantity.