Question

Convert each of following numbers to Binary numbers, showing all steps.

a. (572) 8

b. (1604) 8

c. (1066)10

d. (99)10

e. (80E)16

f. (135AB)16

Answer 1

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 572 to binary
5 => 101
7 => 111
2 => 010
So, in binary 572 is 101111010
Answer: 101111010

b)
Converting 1604 to binary
1 => 001
6 => 110
0 => 000
4 => 100
So, in binary 1604 is 001110000100
Answer: 001110000100

c)
Divide 1066 successively by 2 until the quotient is 0
   > 1066/2 = 533, remainder is 0
   > 533/2 = 266, remainder is 1
   > 266/2 = 133, remainder is 0
   > 133/2 = 66, remainder is 1
   > 66/2 = 33, remainder is 0
   > 33/2 = 16, remainder is 1
   > 16/2 = 8, remainder is 0
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10000101010
So, 1066 of decimal is 10000101010 in binary
Answer: 10000101

d)
Divide 99 successively by 2 until the quotient is 0
   > 99/2 = 49, remainder is 1
   > 49/2 = 24, remainder is 1
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100011
So, 99 of decimal is 1100011 in binary
Answer: 01100011

e)
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 80E to binary
8 => 1000
0 => 0000
E => 1110
So, in binary 80E is 100000001110
Answer: 100000001110

f)
Converting 135AB to binary
1 => 0001
3 => 0011
5 => 0101
A => 1010
B => 1011
So, in binary 135AB is 00010011010110101011
Answer: 00010011010110101011