n301/cs03numbers
n301.tplt
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