1368 Number Systems (on CD) Appendix E E.18 (Cedant web hosting)
1368 Number Systems (on CD) Appendix E E.18 Binary: 512 256 128 64 32 16 8 4 2 1 256 128 64 32 16 8 4 2 1 (1*256)+(1*128)+(0*64)+(1*32)+(0*16)+(0*8)+(0*4)+(0*2)+ (1*1) 110100001 One s complement: 001011110 Two s complement: 001011111 Check: Original binary number + its two s complement 110100001 001011111 000000000 E.19 Zero. EXERCISES E.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 might the highest symbol for the digit in base 12 be? What are the positional values of the rightmost four positions of any number in the base 12 number system? E.21 How is the highest symbol value in the number systems we discussed related to the positional value of the first digit to the left of the rightmost digit of any number in these number systems? E.22 Complete the following chart of positional values for the rightmost four positions in each of the indicated number systems: decimal1000100 10 1 base 6 …… 6… base 13 … 169… … base 3 27……… E.23 Convert binary 100101111010 to octal and to hexadecimal. E.24 Convert hexadecimal 3A7D to binary. E.25 Convert hexadecimal 765F to octal. (Hint: First convert 765F to binary, then convert that binary number to octal.) E.26 Convert binary 1011110 to decimal. E.27 Convert octal 426 to decimal. E.28 Convert hexadecimal FFFF to decimal. E.29 Convert decimal 299 to binary, to octal, and to hexadecimal. E.30 Show the binary representation of decimal 779. Then show the one s complement of 779, and the two s complement of 779. E.31 What is the result when the two s complement of a number is added to itself? E.32 Show the two s complement of integer value -1 on a machine with 32-bit integers.
Visit our web design programs services for an affordable and reliable webhost to suit all your needs.