Question

Representations and Conversions

a) Write the digits for a base 20 system, using an extension of the same digit representation scheme employed for hexadecimal.

b) Convert (2014)10 to base 20

c) Convert (BCI.G)20 to base decimal

Answer 1

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

Step-by-step 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

`= (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 * (1)/(20) )\\= 4400 + 240 + 18 + (16)/(20) \\= 4658 + (16)/(20) \\= 4658 + (4)/(5)\\=(23290 + 4)/(5) \\= (23294)/(5)\\= 4658.8`