Convert 6183300 to hexadecimal base 16 Carry out your answer

Convert (6183.300) to hexadecimal (base 16). Carry out your answers to 3 places past the \"point\".

Solution

Algorithm

For decimal number x:

Get the highest power of 16 that is less than the decimal number x:

16ⁿ < x, (n=1,2,3,...)

The high hex digit is equal to the integer if the decimal number x divided by the highest power of 16 that is smaller than x:

d_n = int(x / 16ⁿ)

Calculate the difference of the number x and the hex digit d_n times the power of 16, 16ⁿ:

= x - d_n × 16ⁿ

Repeat step #1 with the difference result until the result is 0.

Example

Convert x=6183.300 to hexadecimal:

n=3, 16³=4096 < 6183.300

n=4, 16⁴=65536 > 6183.300

So

n = 3

d₃ = int(6183.300 / 16³) = 1

= 6183.300 - 1×16³ = 2087.3

n = 2, x = = 2087.3

d₂ = int(2087.3 / 16²) = 8

= 2087.3 - 8×16² = 39.3

n = 1, x = = 39.3

d₁ = int(39.3 / 16¹) = 2

= 39.3 - 2×16¹ = 7.3

n = 0, x = = 7.3

d₀ = int(7.3 / 16⁰) = 7

= 7.3 – 7.3×16⁰ = 0

(d₃d₂d₁d₀) = 1827