I assume, this is meant as dezimal (since it could not be binary because of the digit 5). To find the equivalents in binary and hex, i can simply convert base and exponent separately from decimal to binary and hex:
15^10 (dec) = F^A (hex) = 1111^1010(bin)
In case it is meant as hex, the answer would be:
15^10(hex) = 21^16(dec) = 10101^10000
I assume, this sgould be decimal (binary is ot possible because of the digit 2):
1011^2 = 3F3^2(hex) = 1111110011^10(bin)
I have converted base and exponent separately. 1024(dec) = 0x400(hex), so 1011(dec) is 13(dec) (or 0xD) less than 0x400, so it is 3F in the first 2 hex digits (one less then the first 2 hex digits 40 of 1024(dec)), and the last hexdigit must be 16(dec)-13(dec) i.e.3. So the base converted to hex is 3F3. 2 is the same in decimal and hex. For conversion to binary, i used the hex values of base and exponent, which can be converted hexdigit for hexdigit to binary, given 001111110011^0010, stripping the leading zeros gives 111110011^10. In case, the original term is meant as hex, the solution will be:
1011^2(hex) = 5013^2(dec) = 1000000010001^2
The biggest question in case it is meant as hex is "what is the decimal equivalent of 0x1011?", and that can be answered with (16*16*16)+16+1 = (256*16)+17 = 4096+17 = 5013
Thiis must be hex, as there is no digit B in decimal or binary.
B^16(hex) =11^22(dec) = 1011^10110(bin)
Conversion between 2 digit hex numbers to decimal and vice versa is possible with a little bit training) without using a calculator or counting fingers ... conversion between hex and binary can be done per hex digit (or from binary to hex with the knowledge, that each block of 4 binary digits is equivalent to exactly one hex digit).
identifying the base number systems in each question is academic.
clearly stated was NOT to try and calculate resulting values.
for question 2) 1011 is in fact binary. ^2 is an exponent represented by the ^. binary has 2 states. you'll note that decimal was already represented in 1) and hex in 3), not only because of the numbers, but because of the exponents.
If the base system in 2) should be binary, the question is wrong (should have read then "1011^10"). But if i assume, that the base in 2) should be 2 and the question 1011^10, the answer should be:
1011^10(bin) = 11^2(dec) = 0xB^2(hex)
In this case, you see, that the values of 2) and 3) are identical. If the question would have been asked with 2) as "1011^10", and the knowledge, that 2 of the values are identical, one could answer the question without calculationg the different representations of exponents.
The only possibility of identical values are the 2) and 3) are identical values, because the first value is much larger than the second (exponent is larger because it is the largets binary value representable in 4 binary digits and the expoent is much larger the the exponent in 1), so 1) and 2) could not be identical). 1) and 3) could also not have been identical, because the base of 3) is also lower than the base of 1, and the exponent is also much less than the exponent of 1), so the values of 1) and 3) could also not have been identical). So the only pair of values, that may be identical would have been 2) and 3) ...
1011^10(bin) = 11^2(dec) = 0xB^2(hex)
warmer, but not quite it...
hint:binary is a base 2 number system
and also, "identical values" was clearly NOT stated.
these 2 were distractor's:
and no exponential peaking; calculator, abacus, et al.
finger counting is allowed (i do it all the time)
these 4 were the endgame:
using binary, decimal and hex, show the question's 2 corresponding number system equivalents.
your equivalents must look like this:
n^x for each corresponding system.
I did not say calculate values.
admittedly, i looked at it for quite a while, and i thought the guy was out of his mind...
then it hit me...
the first number is a number in the particular format of the system, and the second number describes the number system itself.
and that is all.
it made me think of the ccie r&s written blueprint and the evasiveness of its taxonomy, and as i continue forward with lab preparation i can see i am plagued by my own "interpretation bias"
So the "^10" is notthing to calculate but only means "decimal"? So you simply want to convert the values 10(dec), 1011(bin) and B(hex) each to the other 2 bases? So i would just write the converted values, as i can convert such small numbers without doing calculations or counting fingers, i just see the result for numbers, that are in the "one hex digit range":
15(dec) = 1111(bin) = F(hex)
1011(bin) = 11(dec) = B(hex)
B(hex) = 11(dec) = 1011(bin)
You can try to do calculations (maybe with your fingers), to do for example:
1011(bin) = 1*1(dec) + 1*2(dec) + 0*4(dec) + 1*8(dec) = 1(dec) + 2(dec) + 8(dec) = 11(dec)
or calculate the decimal number as sum of powers of 2 to convert the number to binary:
15(dec) = 1*8(dec) + 1*4(dec) + 1*2(dec) + 1*1(dec) = 1111(bin)
But as i wrote above: i don't need that for such small numbers ...
And i wouldn't use the irritating way to write it, that you did. "15^10" is in my opinion the mathematical expression for 15*15*15*15*15*15*15*15*15*15, which can be calculated to 225*225*225*225*225, which i would not calculate by hand without needs ...