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@ -8,7 +8,7 @@ In this handout, we'll denote bit strings with the prefix `0b`. \
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That is, $1010 =$ "one thousand and one," while $#text([`0b1001`]) = 2^3 + 2^0 = 9$
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That is, $1010 =$ "one thousand and one," while $#text([`0b1001`]) = 2^3 + 2^0 = 9$
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#v(2mm)
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#v(2mm)
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We will separate long bit strings with underscores for readability. \
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We will seperate long bit strings with underscores for readability. \
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Underscores have no meaning: $#text([`0b1111_0000`]) = #text([`0b11110000`])$.
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Underscores have no meaning: $#text([`0b1111_0000`]) = #text([`0b11110000`])$.
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#problem()
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#problem()
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@ -1,6 +1,6 @@
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#import "@local/handout:0.1.0": *
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#import "@local/handout:0.1.0": *
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= Bonus -- More about Floats
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= Bonus: More about Floats
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#problem()
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#problem()
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Convince yourself that all numbers that can be represented as a float are rational.
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Convince yourself that all numbers that can be represented as a float are rational.
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@ -8,29 +8,13 @@ Convince yourself that all numbers that can be represented as a float are ration
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#problem()
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#problem()
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Find a rational number that cannot be represented as a float.
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Find a rational number that cannot be represented as a float.
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#v(1fr)
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#problem()
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#problem()
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What is the smallest positive 32-bit float?
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How many floats are between $0$ and $1$?
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#v(1fr)
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#problem()
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What is the largest positive 32-bit float?
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#v(1fr)
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#problem()
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How many floats are between $-1$ and $1$?
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#v(1fr)
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#problem()
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#problem()
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How many floats are between $1$ and $2$?
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How many floats are between $1$ and $2$?
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#v(1fr)
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#problem()
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#problem()
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How many floats are between $1$ and $128$?
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How many floats are between $1$ and $128$?
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#v(1fr)
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