SOLUTION: Change the following base 10 numbers to their binary (base 2) equivalents. 19 __________ 39 ___________ 77 ___________

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Question 270031: Change the following base 10 numbers to their binary (base 2) equivalents.
19 __________ 39 ___________ 77 ___________

Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Change the following base 10 numbers to their binary (base 2) equivalents.
:
Position: 64 32 16 8 4 2 1
:
19: 1 0 0 1 1.__; 39: 1 0 0 1 1 1.__; 77: 1 0 0 1 1 0 1. ___

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Keep dividing by 2, then read the remainders backwards
starting with the final division
19%2F2+=+9 and 1 remainder
9%2F2+=+4 and 1 remainder
4%2F2+=+2 and 0 remainder
2%2F2+=+1 and 0 remainder
(Most significant bit)10011(Least significant bit)
base 2 = 19 base 10
check:
The values of the positions starting with smallest are:
2%5E0
2%5E1
2%5E2
2%5E3
2%5E4
etc., and to read the base-2 number:
2%5E0%2A1+%2B+2%5E1%2A1+%2B+2%5E2%2A0+%2B+2%5E3%2A0+%2B+2%5E4%2A1
1+%2B+2+%2B+0+%2B+0+%2B+16+=+19
Here's some binary numbers:
0000 zero
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
Convert 8 to binary:
8%2F2+=+4 +0
4%2F2+=+2 +0
2%2F2+=+1 +0
Reading it backwards:
1000base 2 = 8 base 10
You can now do the rest of the problems