MHB Convert the following numbers to their floating point binary equivalent.

[shamieh]

Convert the following numbers to their floating point binary equivalent.

Can someone check my work?

a) 18.25

so I got 10010.01

I couldn't find an online conversion calculator anywhere.

can you also check my answer for this one?

b) 1027.375

I got

10000000011.010

 

[HallsofIvy]

Convert the following numbers to their floating point binary equivalent.

Can someone check my work?

a) 18.25

so I got 10010.01

0.25= 1/4 which is "0 times 1/2+ 1 times 1/2^2.
that is, .25= 0.01.
18= 16+ 2= 1(2^4)+ 0(2^3)+ 1(2^2)+ 1(2)+ 0(1)
so 18 is 10110.
Yes, 18.25 is 10110.01 in base 2.

]I couldn't find an online conversion calculator anywhere.

can you also check my answer for this one?

b) 1027.375

I got

10000000011.010

0.375 is 3/8= (2+ 1)/8= 1/4+ 1/8= 0(1/2)+ 1(1/4) + 1(1/8) so that is 0.011
What you have is 0.010= 0(1/2)+ 1(1/4)+ 0(1/8).

1027= 1024+ 3= 2^{10}+ 2+ 1 so that is 10000000011
so 1027.375 is 100000011.011. What you have is the binary expression of 1027.25.

 

[Evgeny.Makarov]

Concerning the floating point, if you mean the IEEE 754 standard, the result depends whether you need single or double precision. I'll quote my response to a similar question from a different forum.

"Understanding IEEE 754 floating-point specification requires some time and effort. You should read your textbook or lecture notes, or at least Wikipedia pages about floating point and single-precision floating-point format.

First you need to convert 176.2058 to binary: 10110000.00110100101011110100111100001100...₂. Next you round it to 24 bits: 10110000.0011010010101111. In the final representation, the decimal point should be after the first bit: 1.01100000011010010101111 * 2⁷. The exponent is stored as the sum of 7 (or whatever it is for a given number) and 127, i.e., 134 in this case. In binary, 134 = 10000110₂. The first bit of significand is always 1, so it is not recorded, which leaves 23 bits. The final representation consists of the sign bit (0 means +1), the exponent and the significand. Thus, it is

0 10000110 01100000011010010101111.

Here are a couple of online calculators that can compute floating-point representation."