Question

Please don’t just write the final answers.

Please show the steps for each question (via text, arrows, grouping, etc)

1. Use the grouping method to convert the following binary number to (a) octal and (b) hexadecimal:

a. 1010110101011₂

2. Use the grouping method to convert the following numbers to binary:

a. 6435₈   - b. 4F1A₁₆

Answer 1

1)
to hexadecimal:
----------------
Adding 3 zeros on left hand side of this number to make it's length a multiple of 4
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from binary to hexadecimal
Converting 0001010110101011 to hexadecimal
0001 => 1
0101 => 5
1010 => A
1011 => B
So, in hexadecimal 0001010110101011 is 0x15AB

to octal:
-----------
Octal        Binary
    0           000
    1           001
    2           010
    3           011
    4           100
    5           101
    6           110
    7           111
Use this table to convert from binary to octal
Converting 001010110101011 to octal
001 =>  1
010 =>  2
110 =>  6
101 =>  5
011 =>  3
So, in octal 001010110101011 is 12653

2)
a)
Octal        Binary
    0           000
    1           001
    2           010
    3           011
    4           100
    5           101
    6           110
    7           111
Use this table to convert from Octal to binary
Converting 6435 to binary
6 => 110
4 => 100
3 => 011
5 => 101
So, in binary 6435 is 110100011101

b)
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from hexadecimal to binary
Converting 4F1A to binary
4 => 0100
F => 1111
1 => 0001
A => 1010
So, in binary 4F1A is 0100111100011010