Lab 2

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Lab 2

• Binary Math

2
Binary Math

• 1110
• 11111
• 1010__100
• Help?

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Basic Facts of Binary Math

• 11 10
• 10 1 01
• 1-1 0
• 101 11
• 10-1 1
• 100-1 11
• Place Values Y2x

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Place Value Its flippin crazy!
Bigger EndSmaller End
2416128
0 1 0 0 1 0 1 1 0
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Advice

• Pencil/eraser
• Show all steps
• Do it all yourself group work wont help much
  when you take the tests by yourself!
• Put commas in every 3 digits to make it clearer
• Take your time

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Yet More Advice

• Keep the columns straight! This is a must to get
  the right answer.
• Convert to base 10 if you need to- careful of
  conversion errors
• Slow and Steady wins the race

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Mixed up Columns
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Conversion Binary-gtDecimal
Bigger EndSmaller End
2416128
0 1 0 0 1 0 1 1 0
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Converting More.

• Base 10 to base n with a number x
• Find the largest power of n that x can be divided
  by, and call that power p. p is going to be the
  left-most slot. Find out how many times np needs
  to be multiplied by to fill that slot. Repeat for
  the next lowest power of n.
• Example below!

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Example 234(base 10)-gtBinary

• 234 can be divided by 128, but not 256. Therefore
  there will be 8 slots. 1282 is 256, so slot 7
  has a 1 written down in it. Subtract 128 from the
  number, giving us 108.
• Why 8? Isnt 12827? Because we need the 0th
  spot.

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Example 234(base 10)-gtBinary

• 106 is our current . 106 has 1 64 in it. We
  write down a 1 in the 64s position. Subtract 64
  from 106. We now have 42.
• 42 has 1 32 in it. We write down a 1 in the
  32s position. Subtract
• 10 has no 16 in it. Write down a 0 in the 16s
  position.
• 1 8, and 1 2, go into 10.