Someone help me convert to binary?

Question

x = 8

x = 12

x = 1.5

x = 1.25

I can do 8 and 12, but if someone would explain the last two I'd appreciate it!

Answer 1

Not too hard. Binary fractions work just like decimal fractions, except each place to the right is 1/2 the value of the previous.

1000 = 8

0100 = 4

0010 = 2

0001 = 1

0.1000 = 1/2

0.0100 = 1/4

0.0010 = 1/8

Answer 2

256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1

Think of those as place holders in binary

2^0, 2^1, 2^2, 2^3...etc.

Since 8 = 2^3, in binary it is (1000)

So for x = 12, (1100)

Treat x = 1.5 as two parts, the integer and the fraction, 1/2

For integers do it as usual; for fractions, multiply by 2 until

remainder = 0

x = 1.5 (1.1) in binary

x= 1.25 is (1.01) in binary.

Answer 3

Consider the digits to the right of the decimal point in a decimal number like 1.25. The two means 2 times 1/10 (or 10 ^ -1) and the five means 5 times 1/100 (or 10 ^ -2).

By that logic, in binary the first digit to the right of the point would be 1/2 (or 2 ^ -1), the second 1/4 (or 2 ^ -2), the third 1/8 (or 2 ^ -3), etc.

So 1.5 in decimal is the same as 1.1 in binary. Likewise, 1.25 in decimal is the same as 1.01 in binary.