Convert 10011 base 2 to a number in base 5

Chemistry

ScanSolve AI Answer

Answer

34534_5

Step-by-step solution

2 steps

Here's how to convert 10011210011_2 to base 5:

  1. Convert the binary number (10011210011_2) to base 10.

    100112=(1×24)+(0×23)+(0×22)+(1×21)+(1×20)10011_2 = (1 \times 2^4) + (0 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) =(1×16)+(0×8)+(0×4)+(1×2)+(1×1)= (1 \times 16) + (0 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) =16+0+0+2+1= 16 + 0 + 0 + 2 + 1 =1910= 19_{10}
  2. Convert the base 10 number (191019_{10}) to base 5.

    Divide 19 by 5 and record the remainders.

    19÷5=3 remainder 419 \div 5 = 3 \text{ remainder } 4 3÷5=0 remainder 33 \div 5 = 0 \text{ remainder } 3

    Reading the remainders from bottom to top gives the base 5 number.

    Therefore, 10011210011_2 in base 5 is 345\boxed{34_5}.

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