The Glass Castle by Jeannette Walls
Tiffany writes:
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Clint notes: The science and math Rex Walls lays on his kids reads pretty soundly it seems to me. On one point I don't agree--the reason stars 'twinkle.' Many stars and other star-like objects pulsate, but on a longer time scale. Stars, even though huge, are so far away they act like point sources of light and can be blocked out by a dust particle in our atmosphere floating across. Just as your finger can blot out a whole house if the house is a distance away. This is what makes stars 'twinkle' sometimes.
Can't believe his laying 'binary number theory' on his daughter but it could be done. For fun (my own) and the remote chance anyone's interest here's a
Binary Number Primer
Binary numbers is a ‘place value’ system just like decimal numbers. The value of ‘places,’ however, go up (right to left) by powers of 2 instead of powers of 10. So, instead of having one’s place, ten’s place, hundred’s place, etc., one has one’s place, two’s place, four’s place, eight’s place, etc.
Example: (Binary) 11101 = (Decimal) 16 + 8 + 4 + 0 + 1 = 29
To convert a decimal number to binary (as apparently Jeanette’s Dad taught her to do), choose the highest power of two contained therein and place a ‘1' in the corresponding binary place. Subtract that much and repeat with the remainder.
Example: 653:
512 is largest power of two therein so put a ‘1' in the 512 place. That leaves 141 and that’s smaller than 256 so put a ‘0' in the 256 place. Put a 1 in the 128 place. That leaves 13, too large for the 64, 32 and 16 places so put zeroes in these three places. Put a ‘1' in the 8's place. That leaves 5 so put a 1 in the 4 place. That leaves 1 so put a ‘0' in the 2 place and a’1' in the 1 place. Result, a ten-place number instead of three as in the decimal version. (Note: All even binaries end in zero and all odd ones end in one.)
1010001101 (Decimal check: 512 + 0 + 128 + 0 + 0 + 0 + 8 + 4 + 0 + 1 = 653)
Addition
Remember having to learn ‘addition facts’===1+2=3...6+7=13...etc. all the way up 9+9=18? I think that’s some 55 ‘facts.’ In binary arithmetic there are only three:
0 + 0 = 0
1 + 0 (or 0 + 1) = 1
1 + 1 = 10 (‘carry’ the ‘1' to the next column)
Example: Adding 16 to 61
Decimal Convert
to binary Decimal
check
16 010000 0 + 16 + 0 + 0
+ 0 + 0 = 16
61 111101
32 + 16 + 8 + 4 + 0 + 1 = 61
Add 77 1001101 64 + 0 + 0
+ 8 + 4 + 0 + 1 = 77
Other binary arithmetic operations, even subtraction, are more complicated for us, brainwashed in the decimal system, but easy for computers.