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Translate the number system from one to another

Please write how you got the answers



Translate the number system from one to another Please write how you got the answers-example-1

1 Answer

5 votes

Answer:

1) 337; 2) 1364; 3) 31.

Step-by-step explanation:

1) 223/8=27*8+7 - the underlined number 7 is in result; the number 27 is in the next step:

27/8=3*8+3 - the underlined number 3 is in result; the number 3 is in the next step:

3 - the number 3 is in result (cannot divided by 8).

Finally, the result is 337₈ (not 733).

2) 2f4₁₆ is possible to imagine in binary: 2₁₆ as 0011₂; f₁₆ as 1111 and 4₁₆ as 0100₂;

then rewrite (0011 1111 0100)₂ as (001 011 110 100)₂, then to convert every group consists of 3 digits: 001₂=1₁₀; 011₂=3₁₀; 110₂=6₁₀ and 100₂=4₁₀.

Finally, (001 011 110 100)₂=1364₁₀.

3) if to divide the given binary number into groups by 3 symbols, then it can be written 11001₂= (11 001)₂ or (011 001)₂. Then if to write every group in dec form, then 011₂=3₁₀ and 001₂=1₁₀.

Finally, (011 001)₂=31₁₀.

PS. note, the given way is not the shortest one.

User Mark Lagendijk
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