Question

Convert from hex to decimal:
a. AA12
b. 23FE.AA

Answer 1

The hexadecimal number AA12 converts to 43538 in decimal, and 23FE.AA converts to 9215.6640625 in decimal. This is accomplished by multiplying each hex digit by the appropriate power of 16, factoring in its position from right to left, with additional calculations for any digits following a decimal point.

Step-by-step explanation:

To convert from hexadecimal (hex) to decimal, each hex digit must be multiplied by the corresponding power of 16, starting from the rightmost digit and moving to the left. Each power corresponds to the position of the digit, starting from 0 for the rightmost digit. The hex digits correspond to decimal values as follows: A=10, B=11, C=12, D=13, E=14, F=15.

Let's convert the given hex numbers to decimal:

1. AA12 in hex to decimal:
2. A (leftmost) = 10 × (16^3)
3. A = 10 × (16^2)
4. 1 = 1 × (16^1)
5. 2 (rightmost) = 2 × (16^0)
6. Now sum the values: (10 × 4096) + (10 × 256) + (1 × 16) + (2 × 1) = 40960 + 2560 + 16 + 2 = 43538
7. 23FE.AA in hex to decimal:
8. 2 = 2 × (16^3)
9. 3 = 3 × (16^2)
10. F = 15 × (16^1)
11. E = 14 × (16^0)
12. . (After decimal point) A = 10 × (16^-1)
13. . (After decimal point) A = 10 × (16^-2)
14. Now sum the values: (2 × 4096) + (3 × 256) + (15 × 16) + (14 × 1) + (10 × 0.0625) + (10 × 0.00390625) = 8192 + 768 + 240 + 14 + 0.625 + 0.0390625 = 9215.6640625