How 7AB in hexadecimal is binary?

Answer 1

Every digit is a power of 16 in hexadecimal, so we have (in decimal):

Keep in mind A = 10, B = 11, ... F = 15.

7AB16 = 7 * 162 + 10 * 16 + 11 = 1792 + 160 + 11 = 1963.

To convert to binary, we look at powers of 2. Since the largest power of two that can be subtracted from 1963 is 1024, we know that we must go from 210 to 20. Thus we subtract the highest power of 2 that can be subtracted each time. In the brackets is the power of 2 that was subtracted.

1963 - 1024 = 939 (210)

939 - 512 = 427 (29)

427 - 256 = 171 (28)

171 - 128 = 43 (27)

43 - 32 = 11 (25)

11 - 8 = 3 (23)

3 - 2 = 1 (21)

1 - 1 = 0 (20)

When you've done this, list all of the powers from 10 to 0 and put a 1 if you did subtract that number.

10 9 8 7 6 5 4 3 2 1 0 Power of 2

..1 1 1 1 0 1 0 1 0 1 1 Was the number subtracted? (ignore the dots, they're used to pad)

Thus the number in binary is 11110101011.