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

2 Answers

(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

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