Express the following hexadecimal numbers into equivalent decimal numbers. (i) 4A2 (ii) 9E1A

Q. Express the following hexadecimal numbers into equivalent decimal numbers.

(i) 4A2

(ii) 9E1A

(iii) 6BD

(iv) 6C.34

Answer: -

(i) Convert the hexadecimal number 4A2 to decimal:

4A2 = (4 * 16^2) + (10 * 16^1) + (2 * 16^0)
= (4 * 256) + (10 * 16) + (2 * 1)
= 1024 + 160 + 2
= 1186

(ii) Convert the hexadecimal number 9E1A to decimal:

9E1A = (9 * 16^3) + (14 * 16^2) + (1 * 16^1) + (10 * 16^0)
= (9 * 4096) + (14 * 256) + (1 * 16) + (10 * 1)
= 36864 + 3584 + 16 + 10
= 40474

(iii) Convert the hexadecimal number 6BD to decimal:

6BD = (6 * 16^2) + (11 * 16^1) + (13 * 16^0)
= (6 * 256) + (11 * 16) + (13 * 1)
= 1536 + 176 + 13
= 1725

(iv) Convert the hexadecimal number 6C.34 to decimal:

6C.34 = (6 * 16^1) + (12 * 16^0) + (3 * 16^-1) + (4 * 16^-2)
= (6 * 16) + (12 * 1) + (3 * 0.0625) + (4 * 0.00390625)
= 96 + 12 + 0.1875 + 0.015625
= 108.203125