How do you find in decimals the ratio ( binary 1.01)/(octal 2.4)?

Sep 25, 2016

(Binary 1.01) /(Octal 2.4) = $0.5$

Explanation:

Binary $1.01$

= Decimal $1 + \frac{0}{2} + \frac{1}{2} ^ 2$

= Decimal $1 + 0 + \frac{1}{4}$

= Decimal $1.25$

Octal $2.4$

= = Decimal $2 + \frac{4}{8}$

= Decimal $2 + \frac{1}{2}$

= Decimal $2.5$

(Binary 1.01) /(Octal 2.4) = $\frac{1.25}{2.5} = 0.5$

Convert to decimal each number...

Explanation:

An floating point expression in a given base can be converted to decimal by following way:

let the base be $b$
right most digit before (at the left of) the point be $n 0$
second one be $n 1$
third one be $n 2$
...and so on $\left(n 3 , n 4 , n 5 \ldots\right)$

now lets take the right side of the point
first digit after (at the right of) point be $m 1$
second one be $m 2$
third one be $m 3$
and so on $\left(m 4 , m 5 , m 6. . .\right)$

then number in decimal is:

$n 0 \cdot {b}^{0} + n 1 \cdot {b}^{1} + n 2 \cdot {b}^{2} + n 3 \cdot {b}^{3} + \left(n 4 \cdot {b}^{4} + n 5 \cdot {b}^{5.} . .\right)$
$+ m 1 \cdot \frac{1}{b} ^ 1 + m 2 \cdot \frac{1}{b} ^ 2 + m 3 \cdot \frac{1}{b} ^ 3 + m 4 \cdot \frac{1}{b} ^ 4 + \ldots$

so the solution is:

(1.01)b= (?)decimal

$1.01 = 1 \cdot {2}^{0} + 0 \cdot {2}^{- 1} + 1 \cdot {2}^{- 2}$

$= 1 + \frac{0}{2} + \frac{1}{4} = \left(1.25\right) \mathrm{de} c i m a l$

$\left(2.4\right) o c t a l = 2 \cdot {8}^{0} + 4 \cdot {8}^{-} 1$
$= 2 + \frac{4}{8} = \left(2.5\right) \mathrm{de} c i m a l$

so expression in decimal is:
$\frac{1.25}{2.5} = \frac{1}{2} = 0.5$