Question

1.Convert hexadecimal number 5EEC into decimal?

2. Convert hexadecimal number 12DD into decimal?

3.Convert hexadecimal number CEEA5 into decimal?

4.Convert hexadecimal number 1FBAE into binary?

5.Convert Octal number 41326 into decimal?
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Answer 1

Answer:

regular decimal number is the sum of the digits multiplied with power of 10.

137 in base 10 is equal to each digit multiplied with its corresponding power of 10:

13710 = 1×102+3×101+7×100 = 100+30+7

Hex numbers are read the same way, but each digit counts power of 16 instead of power of 10.

For hex number with n digits:

dn-1 ... d3 d2 d1 d0

Multiply each digit of the hex number with its corresponding power of 16 and sum:

decimal = dn-1×16n-1 + ... + d3×163 + d2×162 + d1×161+d0×160

Example #1

3B in base 16 is equal to each digit multiplied with its corresponding 16n:

3B16 = 3×161+11×160 = 48+11 = 5910

Example #2

E7A9 in base 16 is equal to each digit multiplied with its corresponding 16n:

E7A916 = 14×163+7×162+10×161+9×160 = 57344+1792+160+9 = 5930510

Example #3

0.8 in base 16:

0.816 = 0×160+8×16-1 = 0+0.5 = 0.510