Question

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

Answer 1

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

Explanation:

Binary `1.01`

= Decimal `1+0/2+1/2^2`

= Decimal `1+0+1/4`

= Decimal `1.25`

Octal `2.4`

= = Decimal `2+4/8`

= Decimal `2+1/2`

= Decimal `2.5`

(Binary 1.01) /(Octal 2.4) = `1.25/2.5=0.5`

Answer 2

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 `n0`
second one be `n1`
third one be `n2`
...and so on `(n3,n4,n5 ...)`

now lets take the right side of the point
first digit after (at the right of) point be `m1`
second one be `m2`
third one be `m3`
and so on `(m4,m5,m6...)`

then number in decimal is:

`n0*b^0 + n1*b^1 + n2*b^2 + n3*b^3 + (n4*b^4 + n5*b^5...)`
`+ m1*1/b^1 + m2*1/b^2 + m3*1/b^3 + m4*1/b^4 + ...`

so the solution is:

`(1.01)b= (?)decimal`

`1.01 = 1*2^0 + 0*2^(-1) + 1*2^(-2)`

`= 1 + 0/2 + 1/4 = (1.25)decimal`

`(2.4)octal = 2*8^0 + 4*8^-1`
`= 2 + 4/8 = (2.5)decimal`

so expression in decimal is:
`1.25/2.5 = 1/2 = 0.5`