Question

1.Convert (FA)₁₆ to decimal

2.Convert (10101110)₂ to decimal.

3.Convert (0.10101)₂ to decimal.

Answer 1

1. To convert (FA)₁₆ to decimal multiply each digit with its power of 16

Hex digits are: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

F = 15, A = 10

15*16¹ + 10*16⁰ = 15*16 + 10*1 = 240 + 10 = 250

Therefore, (FA)₁₆ = 250 in decimal.

2. To convert (10101110)₂ to decimal multiply each digit with its power of 2

Digit	1	0	1	0	1	1	1	0
Power of 2	27	26	25	24	23	22	21	20
Digit * power of 2	128	0	32	0	8	4	2	0

Now, add up the values obtained on multiplying digit and power of 2.

128 + 0 + 32 + 0 + 8 + 4 + 2 + 0 = 174

Therefore (10101110)₂ = 174 in decimal.

3. To convert (0.10101)₂ to decimal multiply each digit before the fractional part with power of 2 and divide each digit of the fractional part with the power of 2.

We have 0 before the fractional part, so we multiply 0 with power of 2 corresponding to its place i.e., 0*2⁰ = 0

Digit	1	0	1	0	1
Power of 2	21	22	23	24	25
Divide each digit by power of 2	1/2 = 0.5	0/4 = 0	1/8 = 0.125	0/16 = 0	1/32 = 0.03125

Now, add up the values

0.5 + 0 + 0.125 + 0 + 0.03125 = 0.65625

To get the decimal value of (0.10101)₂ add the part before the fractional part and the fractional part as obtained above i.e., 0 + 0.65625 = 0.65625

Therefore the decimal valus of (0.10101)₂ is 0.65625