SOLUTION: Convert the following binary numbers to decimal and show your calculations: 10101100011 and 10011111 Convert the following decimal numbers to binary and show your calculations:

Click here to see ALL problems on decimal-numbers

Question 1010652: Convert the following binary numbers to decimal and show your calculations: 10101100011 and 10011111
Convert the following decimal numbers to binary and show your calculations: 7625 and 872
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Convert the following binary numbers to decimal and show your calculations: 10101100011
= 563 in Hex
= 5*256 + 6*16 + 3 = 1280 + 96 + 3
= 1379 decimal
-------------------------
and 10011111
= 9F in Hex
= 9*16 + 15
= 159 decimal
===========================
Convert the following decimal numbers to binary and show your calculations:
7625 - 4096 = 3529 --> 1xxx
INT(3529/256) = 13 --> 1Dxx
(Remainder * 16) = 12 --> 1DCx
Remainder = 9 --> 1DC9 in Hex
--> 1 1101 1100 1001 in Binary
=================================
and 872
872 - 256*3 = 104 --> 3xx
104 - 16*6 = 8 --> 36x
--> 368 Hex
= 0011 0110 1000 in Binary
=================================
The best news is Octal (base 8) seems to have blown over.

Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website!

I think that may be too advanced for you. Here's the more elementary way to do the conversions.

Convert the following binary numbers to decimal and show your
calculations: 10101100011 and 10011111

List the digits in a vertical column, each followed by " + 2�" 1 + 2� 0 + 2� 1 + 2� 0 + 2� 1 + 2� 1 + 2� 0 + 2� 0 + 2� 0 + 2� 1 + 2� 1 + 2� Begin with a 0 after the � on the first row, then an equal sign, then do the calculation and put the answer after another equal sign: 1 + 2�0 = 1 + 0 = 1 0 + 2� 1 + 2� 0 + 2� 1 + 2� 1 + 2� 0 + 2� 0 + 2� 0 + 2� 1 + 2� 1 + 2� Then put that result, 1, after the � on the 2nd row, then do that calculation and put that answer after another equal sign: 1 + 2�0 = 1 + 0 = 1 0 + 2�1 = 0 + 2 = 2 1 + 2� 0 + 2� 1 + 2� 1 + 2� 0 + 2� 0 + 2� 0 + 2� 1 + 2� 1 + 2� Then put that result, 2, after the � on the 3rd row, then do that calculation and put that answer after another equal sign: 1 + 2�0 = 1 + 0 = 1 0 + 2�1 = 0 + 2 = 2 1 + 2�2 = 1 + 4 = 5 0 + 2� 1 + 2� 1 + 2� 0 + 2� 0 + 2� 0 + 2� 1 + 2� 1 + 2� Keep doing that all the way down to the bottom: 1 + 2�0 = 1 + 0 = 1 0 + 2�1 = 0 + 2 = 2 1 + 2�2 = 1 + 4 = 5 0 + 2�5 = 0 + 10 = 10 1 + 2�10 = 1 + 20 = 21 1 + 2�21 = 1 + 42 = 43 0 + 2�43 = 0 + 86 = 86 0 + 2�86 = 0 + 172 = 172 0 + 2�172 = 0 + 344 = 344 1 + 2�344 = 1 + 688 = 689 1 + 2�689 = 1 + 1378 = 1379 Answer = 1379 Now you do the other one the same way.

Convert the following decimal numbers to binary and show your
calculations: 7625

Start by dividing 7625 by 2, getting 3812 with remainder 1 and placing the remainder R=1 out beside the quotient. Then divide the quotient 3812 by 2, getting 1906 with remainder 0 and placing the quotiont R=0 out beside the quotient. Do that all the way down until the quotient is 0. 2)7625 2)3812 R=1 2)1906 R=0 2)953 R=0 2)476 R=1 2)238 R=0 2)119 R=0 2)59 R=1 2)29 R=1 2)14 R=1 2)7 R=0 2)3 R=1 2)1 R=1 2)0 R=1 Now take those remainders in reverse order, that is, from the bottom to the top: 1110111001001 That's the answer. Now you do the other one the same way. Edwin