1. Computer Number Systems
Contents
1) General Concepts
2) Decimal
3) Binary
4) Octal
5) Hexadecimal
6) Conversions
7) HexShip
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2. General Concepts
Number Systems are based on the number they are named.
Base 2 = Binary
Base 8 = Oct
Base 10 = Decimal
Base 16 = Hexadecimal
The highest digit in a number system is always the base – 1
Base 2 highest digit 1
Base 8 highest digit 7
Base 10 highest digit 9
Base 16 highest digit 16
The columns starting at 0 at the left represent numbers to power of 0 of the base and increment by 1 going to the right
Any number in any base to the power of 0 is itself
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3. Decimal Decimal is base 10
The highest digit in decimal is a 9 ( )
The Numbers in the right hand column always represent themselves
The numbers in the next column represent the digit times the base number 10.
Example 47 represents 4X or in a more primitive way ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| || if we counting sticks or deer before we had a number system
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4. Binary Binary is base 2 The highest digit is 1
The numbers in the right hand always represent themselves ( ie 0=0 , 1=1 )
The columns going from right to left represent the powers of 2 incrementing by 1 from right to left
101 in binary represents (1 x 2X2) + (0x2x1) + 1 or |||| | in our primitive way or 5 in base 10 decimal
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5. Octal Octal is base 8 Highest digit is 7 ( 8-1)
The numbers in the rightmost column represent themselves
The numbers in the next column represent the digit x 8 ( ie 70 in octal represents 7X8 +0 = 56 in decimal or ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| | and again could be used to represent anything from apples to deer to children.
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6. Hexadecimal Hexadecimal is base 16
The highest digit is F ( Decimal 15,16 -1)
The rightmost column represents the digit itself
The next column represents the digit x 16
For example 10 in hexadecimal represents 16 in decimal
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7. Hexadecimal Digits
Hexadecimal must introduce new digits not used in decimal since we have digits the are above 9.
In order to do this we must invent new symbols to represent these values.
What better symbols than the first five letters of the alphabet , since we are already familiar with their order
Therefore A= decimal 10, B= decimal 11, C= decimal 12, D=decimal 13, E=decimal 14, decimal 15
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8. Number Systems Equated
Number Systems compared
Hex Dec Oct Bin Hex Dec Oct Bin A B C D E F
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9. HEX and DEC equated Number Systems conversion
16 hex = (1x16) + 6 decimal
3AB hex = (1x16x16) + (10x16) + 11 decimal
REMEMBER each column represents the base number times itself according to the position
For example 100 hexadecimal = (1x16X16) decimal
1000 hexadecimal = 1x16x16x16 decimal
200 = (2x16x16) decimal
2000 = (2x16x16x16) decimal
300 = ? decimal ( you answer )
3000 = ? decimal ( you answer )
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10. Hexadecimal to binary Hexadecimal to binary is easy
Every digit in hexadecimal represents 4 binary
For example A = 1010
AA =
AAA =
AAAA =
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11. Worksheet 1 Fill in the blanks in the Worksheet 1 pdf
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