outline

Notational conventions

• Decimal representation for numerical values using the 10 digits
• The 26 letters for textual information
• Sign/magnitude notation for signed numbers – numbers with a + or – sign
• Decimal notation for real numbers with a decimal point separating the whole number part from the fractional part

Representation of information

• External representation
  - the way humans understand information
  - the way it is entered at a keyboard
• Internal representation
  - the way it is stored in the memory of the computer

Computers

• Externally – computers use decimal digits, sign/magnitude notation and the alphabet
• But computers stores data, internally, using the binary numbering system

Binary

• A base-2 positional numbering system
• The value of a digit depends not only on it absolute value but also on its specific position within a number
• Example: Base 10
  3, 873 is (3*10^3) + (8*10^2) + (7*10^1) + (3*10^0) or
  3000 + 800 + 70 + 3

Base-2

• Same concept applies to base 2
• Consists of two digits 0 and 1, referred to as bits
• Example: Base 2
  111001 is
  (1*2^5) + (1*2^4) + (1*2^3) + (0*2^2) + (0*2^1) + (1*2^0)
  and evaluated to 32 + 16 + 8 + 0 + 0 + 1 = 57

Simple Table

• 2^8	2^7	2^6	2^5	2^4	2^3	2^2	2^1	2^0
  256	128	64	32	16	8	4	2	1

Converting Decimal to Binary

• Understanding how we get there by example
• Convert 67 to binary
  - use the table as a tool for conversion