Binary
In mathematics and digital electronics, a binary numberA unit of abstract mathematical system subject to the laws of arithmetic. is a numberA unit of abstract mathematical system subject to the laws of arithmetic. 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
This is one of the better videos I've seen on binary. Content gratefully used with permission : ^{[2]}
Basic Definitions
- 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 numberA unit of abstract mathematical system subject to the laws of arithmetic. 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
I find it helpful to drawRepresent 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. 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 |
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A helpful cheat sheet
How to add two binary numbers
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
You must be able to correctly answer the following questions:
- DefineGive the precise meaning of a word, phrase, concept or physical quantity. the term: bit
- DefineGive the precise meaning of a word, phrase, concept or physical quantity. the term: byte
- DefineGive the precise meaning of a word, phrase, concept or physical quantity. the term: binary
- DefineGive the precise meaning of a word, phrase, concept or physical quantity. the term: denary/decimal (they refer to the same thing)
- DefineGive the precise meaning of a word, phrase, concept or physical quantity. the term: hexadecimal
Why is this so important?
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
Click here for a slide deck that covers this topic nicely