Why Study Binary

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Why Study Binary
In a digital computer all information is
represented using the binary number
system. Simply because it is easy to build
electronic circuits which operate on the basis of
two states, either on or off.
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Number Systems (1)
For example the decimal number 711 is made up of
the following
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Number Systems (2)
Arithmetic
carry
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Number Systems (3)
Range
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What is Binary (1)?

• Currently we are used to a base 10 system called
  denary
• an alternative number system based on 2 is called
  binary
• Works in the same way as denary in that each
  column from right to left indicates an increasing
  power of 2

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What is Binary (2)?

• in denary (10) we have the digits 0 ? 9 available
• Similarly in binary (2) the digits 0 ? 1 are
  available
• a binary number would look like this
• 01101

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Binary Evaluation
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Binary Examples
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Converting to Binary

• Three main methods
• Keep dividing by two and the remainder forms the
  number.
• Keep subtracting decreasing powers of 2.
• Look and guess (subtraction).

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Successive Division
Convert 67 base 10 to base 2
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Subtraction
This gives 1000011
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Octal Notation
Binary is rather inconvenient to read and write
for humans. Octal base 8 only contains digits
0 7 3 binary digits 1 octal digit. Using
01011101 Now try 11111111
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Hexadecimal Notation (1)
An alternative to both binary and octal is
hexadecimal notation. Uses base 16
(hexadecimal) i.e. 0 .. 9, A. B, C, D, E and F 4
binary digits can be represented using 1 hex
digit. e.g. 01001001 11111111
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Hexadecimal Notation (2)
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Other Number Systems
Convert 67 base 10 to base 4