Answer:
b) To convert a number from base b to base 10, we can use the formula:
anbn-1 + an-1bn-2 + ... + a1b0
where ai is the ith digit of the number in base b, and n is the number of digits.
Using this formula for 23₁0:
2×b^2 + 3×b^1 + 0×b^0 = 25
2b^2 + 3b = 25
This equation is not solvable because there are two unknowns (b^2 and b) and only one equation.
c) Using the same formula as above for b2,=2b1:
b^2×2 + b×1 = 2b + 1
b^2×2 - b×2 + b×3 - 2b - 1 = 0
2b^2 + b - 1 = 0
Using the quadratic formula, we find:
b = (-1 ± sqrt(1 + 8×2))/4
b = (-1 ± 3)/4
b = -1/2 or b = 1
However, b must be a positive integer, so the only solution is b = 1.
a) Adding numbers in binary:
111
+101
+110
1010
So 111, +101,+ 110, in binary, equals 1010 in binary, which is equal to 10 in base 10.