Find the numeral to put in the blank to make each equation true. do not convert to base ten
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Find the numeral to put in the blank to make each equation true. do not convert to base ten

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
in bases > 10,10 = A, 11 = B, etc.........
a)342(base five) - _____ = 213(base five)
b)1101(base two) - ____ = 1011(base two)
c)E08(base 12) - ______ = 9(base 12)
d)100(base 2) + ______ = 10000(base 2)

also please explain to me where the number comes in during c, what that means

-
a)

342₅ − ___ = 213₅
___ = 342₅ − 213₅ = 124₅

3 4 2₅
2 1 3₅
--------

2 is less than 3, so we borrow from next column

3 3 ¹2₅
2 1 3₅ ----> 12₅ − 2₅ = 10₅ = 5 -----> 5 − 2 = 3 -----> 12₅ − 4₅ = 3₅
---------
1 2 4₅
______________________________

b)

1101₂ − ____ = 1011₂
____ = 1101₂ − 1011₂ = 0010₂

c)

Is E in E08 supposed to be digit 11 ???
Usually, in bases > 10, we use the following
10 = A, 11 = B, etc...
Otherwise, in the fairly common base 16, we'd have
10 = T, 12 = T, 14 = F, 15 = F
Also, it's easier to do calculations if consecutive digits
are represented by consecutive letters

E08₁₂ − ___ = 9₁₂
___ = E08₁₂ − 9₁₂ = TEE₁₂

Or more commonly B08₁₂ − 9₁₂ = ABB₁₂

d)

100₂ + ____ = 10000₂
____ = 10000₂ − 100₂ = 1100₂

Mαthmφm
1
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