Question

Please show all work:

Multiplying the binary number below by decimal 128 yields ________  

1 0 0 1 1 0 0 1 0 . 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1

1. 1 0 0 . 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1
2. 1 0 0 1 1 . 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1
3. 1 0 0 1 1 0 . 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1
4. 1 0 0 1 1 0 0 1 0 1 1 1 1 1 . 0 1 0 0 0 0 1 1 0 0 1
5. 1 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 . 0 0 0 0 1 1 0 0 1
6.       None of the above

Answer 1

Multiplying the binary number below by decimal 128 yields ________  

1 0 0 1 1 0 0 1 0 . 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1

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The given binary number should be first converted to decimal before multiplying with 128.

hence, 1 0 0 1 1 0 0 1 0 . 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 can be converted to decimal as shown.

1*2^8 + 0*2^7 + 0*2^6 + 1*2^5 + 1*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 0*2^0 + 1*2^(-1) + 1*2^(-2) + 1*2^(-3) + 1*2^(-4) + 1*2^(-5) + 0*2^(-6) + 1*2^(-7) + 0*2^(-8) + 0*2^(-9) + 0*2^(-10) + 0*2^(-11) + 1*2^(-12) + 1*2^(-13)+ 0*2^(-14)+ 0*2^(-15) + 1*2^(-16)

After calculation, it will result in 306.9769439697265625

Now, since both the multiplying values are in decimal, we can muliply them:

i.e, 306.9769439697265625 * 128 = 39293.048828125

The resulting value should now be converted to binary.

The result 39293.048828125 can be converted to binary as follows:

(divide integer portion 39293 by 2 and keep track of the remainder)

(multiply the fractional portion .048828125 by 2 and keep track of integer part)

Please check this image for conversion:

Hence the answer to the question is OPTION e

1001100101111101.000011001