Question

Indices, Surd and Numeral Systems #1
Question 40bii (modified)

How to convert a binary number into hexadecimal number without converting it into decimal number?
Eg: \(1111001110_2\)

Answer 1

1 hex digit takes 4 binary digits

Answer 2

Yes. I understand that. But what should I do next?

Answer 3

0011 1100 1110
3 C E

Answer 4

group into sets of 4
change each set into a hex number

Answer 5

im sure theres a mathical thing that can happen; but they only really differ from 10 to 15

Answer 6

How do you find : 0011 ?

Answer 7

0011 = 3 in binary; so it equals 3 in hex

Answer 8

from 0 to 9 hex and decimals are the same; they differ at 10 - 15 (A - F)

Answer 9

splitting the binary into groups of 4, starting from the right side, is helpful

Answer 10

So, in my example 1111001110

First, group them with 4 digits, counted from the right to the left
11 1100 1110
Since there are insufficient number for the first group, add enough zeros to make it a group of 4. Then it becomes
0011 1100 1110

For the first group,
0011 = 2^2 + 1 = 3 <- first digit of the hex. number

For the second group,
1100 = 2^3 + 2^2 = 12 = C <- second digit in the hex. number

For the third group,
1110 = 2^3 + 2^2 +2 = 14 = E <- last digit in the hex. number

So, the final answer is \(1111001110_2 = 3CE_{16}\)
Is this the case?

Answer 11

thats the case

Answer 12

Thanks!