Sun Coast Amateur
Radio Club Society

User Tools

Site Tools

You are here: home » hambasics » sections » mathbasics
hambasics:sections:mathbasics

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
hambasics:sections:mathbasics [2025/06/25 20:23] – va7fihambasics:sections:mathbasics [2025/06/25 22:51] (current) – [Metric Prefix] va7fi
Line 3: Line 3:
 A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit.
  
-In the previous section, we saw that Mhz means a million Hertz.  Here's a list of the most common ones:+In the previous section, we saw that MHz means a million Hertz.  Here's a list of the most common ones:
  
 <WRAP indent> <WRAP indent>
Line 103: Line 103:
  
 {{ youtube>3Dry9HUSkTo }} {{ youtube>3Dry9HUSkTo }}
 +
  
 ===== Alternative Formulation ===== ===== Alternative Formulation =====
Line 126: Line 127:
  
 ===== dBm ===== ===== dBm =====
 +
 A related measurement is the dBm.  While the decibel (dB) is a ratio between two quantities (saying "20 dB" is the same as saying "100 times more"), the dBm is a ratio between one quantity and 1 mW.  That is, it's a measures of how much stronger (or weaker) the power of something is compared to 1 milliwatt. A related measurement is the dBm.  While the decibel (dB) is a ratio between two quantities (saying "20 dB" is the same as saying "100 times more"), the dBm is a ratio between one quantity and 1 mW.  That is, it's a measures of how much stronger (or weaker) the power of something is compared to 1 milliwatt.
  
Line 134: Line 136:
  
 Notice how the minus sign in front of the dBm means that the power is less (not more) so it divides (not multiply). Notice how the minus sign in front of the dBm means that the power is less (not more) so it divides (not multiply).
 +
  
 ====== Binary Numbers ====== ====== Binary Numbers ======
Line 162: Line 165:
  
 ===== Base 2 ===== ===== Base 2 =====
-Now let's do the same thing again in base 2.  Imagine we only have two symbols we can use to count: 0 and 1.  Let's see what counting to thirteen looks like starting at zero:+Now let's do the same thing again in base 2.  Imagine we only have two symbols we can use to count: 0 and 1.  Let's see what counting to fifteen looks like starting at zero:
  
 <WRAP centeralign> <WRAP centeralign>
-0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101+0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111
 </WRAP> </WRAP>
  
 Do you see the pattern?  Here's another way of writing it with leading zeros and keeping track of where we are in base 10: Do you see the pattern?  Here's another way of writing it with leading zeros and keeping track of where we are in base 10:
-<WRAP prewrap center 10em>+<WRAP indent>
 ^Base 2 ^ Base 10 | ^Base 2 ^ Base 10 |
 |0000   | 0       | |0000   | 0       |
Line 185: Line 188:
 |1100   | 12      | |1100   | 12      |
 |1101   | 13      | |1101   | 13      |
 +|1110   | 14      |
 +|1111   | 15      |
 </WRAP> </WRAP>
  
-You see what I mean about being able to count without knowing how big the number is?  If we wanted, we could count to 1001010011010 and have no idea of how big that number is unless we kept track of it in base 10.  That's because over the years, we developed a number sense for base 10 numbers, but we didn't for base 2 numbers since we don't typically use them.+You see what I mean about being able to count without knowing how big the number is?  All we're doing is "flipping bits" from 0 to 1 in the right order.  If we wanted, we could count to 1001010011010 and have no idea of how big that number is unless we kept track of it in base 10.  That's because over the years, we developed a number sense for base 10 numbers, but we didn't for base 2 numbers since we don't typically use them.
  
 ===== Conversion ===== ===== Conversion =====
Line 217: Line 222:
 Converting the other way around is a bit different, but kind of makes sense if you think about it.  Here are the steps to convert \$ 13_{10} \$ back to \$1101_2\$ and I'll explain a bit more after: Converting the other way around is a bit different, but kind of makes sense if you think about it.  Here are the steps to convert \$ 13_{10} \$ back to \$1101_2\$ and I'll explain a bit more after:
  
-<WRAP prewrap center 35em>+<WRAP indent>
 ^ Division by 2 ^In Decimal ^As fraction           ^ Quotient ^ Remainder ^ ^ Division by 2 ^In Decimal ^As fraction           ^ Quotient ^ Remainder ^
 |13÷2            | 6.5       |6 + \$\frac{1}{2}\$  | 6        | 1         | |13÷2            | 6.5       |6 + \$\frac{1}{2}\$  | 6        | 1         |
Line 250: Line 255:
 Let's look at a trivial example converting 2037 from base 10 to base 10 (trivial indeed!): Let's look at a trivial example converting 2037 from base 10 to base 10 (trivial indeed!):
  
-<WRAP prewrap center 35em>+<WRAP indent>
 ^ Division by 10 ^In Decimal   ^As fraction             ^ Quotient ^ Remainder  ^ ^ Division by 10 ^In Decimal   ^As fraction             ^ Quotient ^ Remainder  ^
 |2037÷10         |203.7        |203 + \$\frac{7}{10}\$  | 203      | 7          | |2037÷10         |203.7        |203 + \$\frac{7}{10}\$  | 203      | 7          |
Line 273: Line 278:
           &= 63003_{10}           &= 63003_{10}
 \end{align*} \end{align*}
 +
 +One reason why hexadecimal is so useful in computer science is because one hexadecimal "digit" can represent four binary "digits".  For example,
 +<WRAP indent>
 +^  Decimal ^  Hexadecimal ^      Binary ^
 +|        1 |            1 |           1 |
 +|        2 |            2 |          10 |
 +|        3 |            3 |          11 |
 +|        4 |            4 |         100 |
 +|  ...                                |||
 +|        7 |            7 |         111 |
 +|        8 |            8 |        1000 |
 +|  ...                                |||
 +^       15 ^            F ^        1111 |
 +|       16 |           10 |      1 0000 |
 +|  ...                                |||
 +|       31 |           1F |      1 1111 |
 +|       32 |           20 |     10 0000 |
 +|  ...                                |||
 +|       63 |           3F |     11 1111 |
 +|       64 |           40 |    100 0000 |
 +|  ...                                |||
 +|      127 |           7F |    111 1111 |
 +|      128 |           80 |   1000 0000 |
 +|  ...                                |||
 +^      255 ^           FF ^        1111 1111 |
 +|      256 |          100 |      1 0000 0000 |
 +|  ...                                     |||
 +^     4095 ^          FFF ^   1111 1111 1111 |
 +|     4096 |         1000 | 1 0000 0000 0000 |
 +
 +</WRAP>
  
 [[wavemodulation |{{/back.png }}]] [[codes |{{  /next.png}}]] [[wavemodulation |{{/back.png }}]] [[codes |{{  /next.png}}]]
hambasics/sections/mathbasics.1750908239.txt.gz · Last modified: by va7fi