F.2 Maths

1) A and B are two consecutive numbers for B < A, so A = B + 1 ... (1)
Half of B exceeds one-fourth of A by 1, so B/2 - A/4 = 1 ... (2)
Put (1) into (2), we have
B/2 - (B + 1)/4 = 1
2B - (B + 1) = 4
B - 1 = 4
B = 5
A = B + 1 = 5 + 1 = 6
The values of A and B are 6 and 5 respectively.
We can check that 5/2 - 6/4 = 2.5 - 1.5 = 1

2.
a) 1101 (2) = 1 * 2^0 + 0 * 2^1 + 1 * 2^2 + 1 * 2^3 = 13 (10)
b) F99D (16) = 13 * 16^0 + 9 * 16^1 + 9 * 16^2 + 15 * 16^3 = 63901 (10)

3. 110 (2) = 0 * 2^0 + 1 * 2^1 + 1 * 2^2 = 0 + 2 + 4 = 6 (10)

4a) 9 = 8 + 1 = 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0 = 1001 (2)
b) 35 = 32 + 2 + 1 = 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 100011 (2)

5a) 4E6B (16)
= 11 * 16^0 + 6 * 16^1 + 14 * 16^2 + 4 * 16^3
= 11 + 96 + 3584 + 16384
= 20075 (10)
b) 4C59 (16)
= 9 * 16^0 + 5 * 16^1 + 12 * 16^2 + 4 * 16^3
= 9 + 80 + 3072 + 16384
= 19545 (10)