Asked by Anonymous

Write the following numbers in the requested bases.
a. 10=_________base 2
b. 42=_________base 2
c. 10101011 base 2=________base 10
d. 77=_______base 5
e. 40 base 6=_______base 10
Answered by Damon
base 2
1 = 2^0 which is 1 decimal (anything^0=1)
1 0 = 2^1 which is 2 decimal
1 0 0 = 2^2 which is 4 decimal
1 0 0 0 = 2^3 which is 8 decimal

1 + n zeros = 2^n

so
a. 10 = 8 + 2 decimal
8 is 2^3 1 0 0 0
2 is 2^1 0 0 1 0
so the answer is
1 0 1 0

b. 42 = 32 + 10 (we already know 10)
32 = 2^5 = 1 0 0 0 0 0
10 = __________1 0 1 0
so the answer is
1 0 1 0 1 0

c.
2^7 +0 + 2^5 +0 +2^4 +0 +0 +2^1 +2^0
128+32+16+2+1 = 179

d. 5^0=1
1 = 5^0
10 = 5^1
100 = 5^2 = 25
1000 = 5^3 = 125 ...
1 + n zeros = 5^n
well 77 = 3*25 + 2
= 3*5^2 + 2 * 5^0
3 0 0 + 2
3 0 2

e. 1 = 6^0
1 0 = 6^2 = 36
1 0 0 = 6^3 = 216 ....
so 4 0 is 4 * 36
which is 144


Answered by Damon

e.
1 = 6^0
1 0 = 6^1 = 6
1 0 0 = 6^2 = 36
1 0 0 0 = 6^3 =216
so 40 is 4*6 or 24
Answered by Reiny
ARRGHHHH!!!!

Unless you are studying Computer Science and are working in base 2, 8 or 16, tell your teacher to quit teaching this silly stuff and get back to real Mathematics.

Tell him/her that an old mathteacher with over 33 years experience said so.

(sorry about the political bias)
Answered by Damon
LOL - well I think it is fun !
Answered by Damon
Had an extra 0 when I copied
c. 10101011 base 2=________base 10
2^7+0+2^5+0+2^3+0+2^1+2^0
128+32+8+2+1
= 171
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