How to convert fractions and decimal numbers into binary notation? E.g 4 1/2, 5/16, 4.7 etc?

4 Answers

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  • Jim
    Lv 7
    2 years ago
    Favourite answer

    You need to know how Positional Value works

    Base 10

    1 x 10^2 = 100

    1 x 10^1 = 10

    1 x 10^0 = 1

    1 x 10-1 = 1/10 = 0.1

    1 x 10-2 = 1/100 = 0.01

    etc

    Base 2: (or any other base follows same design)

    1 x 2^2 = 4

    1 x 2^1 = 2

    1 x 2^0 = 1

    1 x 2-1 = 1/2 = 0.5

    1 x 2-2 = 1/4 = 0.25

    etc

    You simply add up the numbers that give you your value.

    4.5 is 1x2^2 + 0x2^1 + 0.2^0 + 1x2^-1 = 100.1₂

  • ?
    Lv 7
    2 years ago

    4 1/2 = 9/2

    9 = 1001 base 2

    /2 is right shift 1 bit

    4 1/2 = 100.1 base 2

    5/16

    5 = 0101

    /16 is right shift 4 bits

    5/16 = 0.0101

    4.7 does not have an exact representation

    4 = 100 base 2

    fractional part

    2(0.7) = 1.4

    2(.4) = 0.8

    2(.8) = 1.6

    2(.6) = 1.2

    2(.2) = 0.4

    2(.4) = 0.8

    7/10 = 1 0110 0110 ...

    4.7 = 100.0 0110 0110 ...

  • khalil
    Lv 7
    2 years ago

    0.abc

    as you know a, b, and c are 0 or 1

    the values

    a ...1/2

    b ....1/4

    c......1/8

    so on

    1/2 → 0.100

    4 → 100

    4 1/2 = 100.1

  • 2 years ago

    Think of it this way: in the decimal system, the places are:

    with n = 0 to 9 as the digits

    1st = n*10^(-1)

    2nd = n*10^(-2)

    etc

    so, for binary, it would be (n = digits 0, 1)

    1st = n*2^-1

    2nd = n*2^-2

    3rd = n^2^-3

    ...

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