Free web hosts - 1366 Number Systems (on CD) Appendix E TERMINOLOGY
1366 Number Systems (on CD) Appendix E TERMINOLOGY base digit base 2 number system hexadecimal number system base 8 number system negative value base 10 number system octal number system base 16 number system one s complement notation binary number system positional notation bitwise complement operator (~) positional value conversions symbol value decimal number system two s complement notation SELF-REVIEW EXERCISES E.1 The bases of the decimal, binary, octal, and hexadecimal number systems are , , and respectively. E.2 In general, the decimal, octal, and hexadecimal representations of a given binary number contain (more/fewer) digits than the binary number contains. E.3 (True/False) A popular reason for using the decimal number system is that it forms a convenient notation for abbreviating binary numbers simply by substituting one decimal digit per group of four binary bits. E.4 The (octal / hexadecimal / decimal) representation of a large binary value is the most concise (of the given alternatives). E.5 (True/False) The highest digit in any base is one more than the base. E.6 (True/False) The lowest digit in any base is one less than the base. E.7 The positional value of the rightmost digit of any number in either binary, octal, decimal, or hexadecimal is always . E.8 The positional value of the digit to the left of the rightmost digit of any number in binary, octal, decimal, or hexadecimal is always equal to . E.9 Fill in the missing values in this chart of positional values for the rightmost four positions in each of the indicated number systems: decimal 1000 100 10 1 hexadecimal … 256 … … binary … … … … octal 512 … 8 … E.10 Convert binary 110101011000 to octal and to hexadecimal. E.11 Convert hexadecimal FACE to binary. E.12 Convert octal 7316 to binary. E.13 Convert hexadecimal 4FEC to octal. (Hint: First convert 4FEC to binary then convert that binary number to octal.) E.14 Convert binary 1101110 to decimal. E.15 Convert octal 317 to decimal. E.16 Convert hexadecimal EFD4 to decimal. E.17 Convert decimal 177 to binary, to octal, and to hexadecimal. E.18 Show the binary representation of decimal 417. Then show the one s complement of 417, and the two s complement of 417.
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