1. Convert the binary number 111000111 into the base ten equivalent.
1 1 1 0 0 0 1 1 1
1*28 + 1*27 + 1*26 + 0*25 + 0*24 + 0*23 + 1*22 + 1*21 + 1*20
258 + 128 + 64 + 0 + 0 + 0 + 4 + 2 + 1 = 457
2. Convert the base ten number 111 into the binary equivalent.
Keep dividing by 2 putting the quotients underneath and the
remainder out to the right beside the quotient. Quit when
the quotient becoms 0. Then the digits of the binary number
are the remainders reading from bottom to top:
2)111
2)55 1
2)27 1
2)13 1
2)6 0
2)3 1
2)1 1
0 1
List the remainders from bottom to top
Answer: 1110111
3. Convert the decimal number 0.35743574357435743574357435743574...
to a fraction
N = 0.35743574357435743574357435743574...
There are four repeating digits so multiply both sides by 104 or 10000
10000N = 3574.3574357435743574357435743574...
Subtract the original equation for N
10000N = 3574.35743574357435743574357435743574...
N = 0.35743574357435743574357435743574...
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9999N = 3574
N = It doesn't reduce.
Edwin