Convert 1AC in hexadecimal into a decimal number.

Convert 1AC in hexadecimal into a decimal number.

428
424
408
420
This question was previously asked in
UPSC CISF-AC-EXE – 2020
To convert a hexadecimal number (base 16) to a decimal number (base 10), we multiply each digit by its corresponding power of 16 and sum the results. The hexadecimal number is 1AC.
Starting from the rightmost digit, the powers of 16 are $16^0, 16^1, 16^2$, and so on.
In hexadecimal, A represents 10, B represents 11, C represents 12.
$1AC_{16} = 1 \times 16^2 + A \times 16^1 + C \times 16^0$
$ = 1 \times 256 + 10 \times 16 + 12 \times 1$
$ = 256 + 160 + 12$
$ = 416 + 12 = 428$.
The decimal equivalent is 428.
– Hexadecimal uses digits 0-9 and letters A-F to represent values 0-15.
– Conversion to decimal involves summing products of digits and powers of the base (16).
– The position of the digit determines the power of 16.
Hexadecimal is often used in computing as a compact representation of binary data because $16 = 2^4$, meaning each hexadecimal digit represents exactly four binary bits.