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### Exercises

D.20

Some people argue that many of our calculations would be easier in the base 12 number system because 12 is divisible by so many more numbers than 10 (for base 10). What is the lowest digit in base 12? What would be the highest symbol for the digit in base 12? What are the positional values of the rightmost four positions of any number in the base 12 number system?

D.21

Complete the following chart of positional values for the rightmost four positions in each of the indicated number systems:

 decimal 1000 100 10 1 base 6 ... ... 6 ... base 13 ... 169 ... ... base 3 27 ... ... ...

D.22

Convert binary 100101111010 to octal and to hexadecimal.

D.23

D.24

Convert hexadecimal 765F to octal. [Hint: First convert 765F to binary, then convert that binary number to octal.]

D.25

Convert binary 1011110 to decimal.

D.26

Convert octal 426 to decimal.

D.27

D.28

Convert decimal 299 to binary, to octal and to hexadecimal.

D.29

Show the binary representation of decimal 779. Then show the one's complement of 779 and the two's complement of 779.

D.30

Show the two's complement of integer value 1 on a machine with 32-bit integers. 