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rebelmaths

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There is a video on converting decimal to binary below:

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https://www.youtube.com/watch?v=H4BstqvgBow

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First list the powers of 2 $2^0=1,2^1=2,2^2=4,2^3=8,2^4=16,2^5=32...$ 

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(a)  

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We can note that $\\var{ans1}=(\\var{b2}\\times4)+(\\var{b3}\\times2)+(\\var{b4}\\times1)$,

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So, the answer is $\\var{b2}\\var{b3}\\var{b4}$.

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An alternative method to convert from decimal to binary is to repeatedly divide by 2, noting the remainder at each stage. Writing these remainders in reverse order then gives the binary representation of the number.

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$\\var{ans1}\\div 2 = \\var{floor(ans1/2)}$  rem  $\\var{mod(ans1,2)}$

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$\\var{floor(ans1/2)}\\div 2 = \\var{floor(floor(ans1/2)/2)}$  rem  $\\var{mod(floor(ans1/2),2)}$

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$\\var{floor(floor(ans1/2)/2)}\\div 2 = \\var{floor(floor(floor(ans1/2)/2)/2)}$  rem  $\\var{mod(floor(floor(ans1/2)/2),2)}$

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Writing these remainders in reverse order gives a final answer of $\\var{mod(floor(floor(ans1/2)/2),2)}\\var{mod(floor(ans1/2),2)}\\var{mod(ans1,2)}$

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(b)

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 $\\var{ans2}=(\\var{b1}\\times16)+(\\var{b2}\\times8)+(\\var{b3}\\times4)+(\\var{b4}\\times2)+(\\var{b5}\\times1)$,

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So, the answer is $\\var{b1}\\var{b2}\\var{b3}\\var{b4}\\var{b5}$

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An alternative method to convert from decimal to binary is to repeatedly divide by 2, noting the remainder at each stage. Writing these remainders in reverse order then gives the binary representation of the number.

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$\\var{ans2}\\div 2 = \\var{floor(ans2/2)}$  rem  $\\var{mod(ans2,2)}$

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$\\var{floor(ans2/2)}\\div 2 = \\var{floor(floor(ans2/2)/2)}$  rem  $\\var{mod(floor(ans2/2),2)}$

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$\\var{floor(floor(ans2/2)/2)}\\div 2 = \\var{floor(floor(floor(ans2/2)/2)/2)}$  rem  $\\var{mod(floor(floor(ans2/2)/2),2)}$

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$\\var{floor(floor(floor(ans2/2)/2)/2)}\\div 2 = \\var{floor(floor(floor(floor(ans2/2)/2)/2)/2)}$  rem  $\\var{mod(floor(floor(floor(ans2/2)/2)/2),2)}$

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$\\var{floor(floor(floor(floor(ans2/2)/2)/2)/2)}\\div 2 = \\var{floor(floor(floor(floor(floor(ans2/2)/2)/2)/2)/2)}$  rem  $\\var{mod(floor(floor(floor(floor(ans2/2)/2)/2)/2),2)}$

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Writing these remainders in reverse order gives a final answer of $\\var{mod(floor(floor(floor(floor(ans2/2)/2)/2)/2),2)}\\var{mod(floor(floor(floor(ans2/2)/2)/2),2)}\\var{mod(floor(floor(ans2/2)/2),2)}\\var{mod(floor(ans2/2),2)}\\var{mod(ans2,2)}$

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(c)

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$\\var{ans3}=(\\var{b1}\\times128)+(\\var{b2}\\times64)+(\\var{b3}\\times32)+(\\var{b4}\\times16)+(\\var{b5}\\times8)+(\\var{b6}\\times4)+(\\var{b7}\\times2)+(\\var{b8}\\times1)$

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So, the answer is $\\var{b1}\\var{b2}\\var{b3}\\var{b4}\\var{b5}\\var{b6}\\var{b7}\\var{b8}$.

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Convert the number $\\var{ans1}$ to binary.

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 [[0]]

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Convert the number $\\var{ans2}$ to binary.

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[[0]]

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Convert the number $\\var{ans3}$ to binary.

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Answer the following questions putting a 1 or 0 in each box.

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