Binary

[Guest]

Fractions can be written in binary form. Change 101.01 to binary. Give a detailed explanation.

Unsure how to solve.

[Guest]

[tex]101[/tex] (binary) means [tex]1×2^2+0×2^1+1×2^0 = 4 + 0 + 1 = 5[/tex]
[tex]0.01​[/tex] (binary) means [tex]0×2^{−1}+1×2^{−2} = 0 + 0.25=0.25[/tex]
Answer is [tex]5.25[/tex]

[Guest]

I don't understand why you multiplied by 2 with the exponent.

[Guest]

Binary numbers use only two digits: 0 and 1. Each digit in a binary number represents a power of 2, just as each digit in a decimal (base-10) number represents a power of 10.

[Guest]

How do you obtain what the 101 and .01 means in binary ?

[Guest]

Please reply, Thanks.