Answer:
a) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J
b) (2014)10 = (50E)20
c) (BCI.G)20 = 4658.8 in decimal
Explanation:
a) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J
where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15, G = 16, H = 17, I = 18, J = 19
b) (2014)10 to base 20
We will divide by 20
2014 ÷ 20 = 100 remainder 14 (E)
100 ÷ 20 = 5 remainder 0
5 ÷ 20 = 0 remainder 5
Reading the remainder bottom-up, we have 50E
Therefore, (2014)10 = (50E)20
c) (BCI.G)20 to decimal
Giving each digit an index we have:
B = 2
C = 1
I = 0
and G = -1 (since it occur after the decimal point)
B = 11, C = 12, G = 16, I = 18
[tex]= (B * 20^{2}) + (C * 20^{1}) + (I * 20^{0}) + (G * 20^{-1})\\= (11 * 20^{2}) + (12 * 20^{1}) + (18 * 20^{0}) + (16 * 20^{-1})\\= (11 * 400) + (12 * 20) + (18 * 1) + (16 * \frac{1}{20} )\\= 4400 + 240 + 18 + \frac{16}{20} \\= 4658 + \frac{16}{20} \\= 4658 + \frac{4}{5}\\=\frac{23290 + 4}{5} \\= \frac{23294}{5}\\= 4658.8[/tex]
