Chapter 2: Binary Values and Number Systems EXERCISES For Exercises 1-5, match the following numbers with their definition. A. Number B. Natural number C. Integer number D. Negative number E. Rational number 1. A unit of an abstract mathematical system subject to the laws of arithmetic 2. A natural number, a negative of a natural number, or zero 3. The number zero and any number obtained by repeatedly adding one to 4. An integer or the quotient of two integers (division by zero excluded) 5. A value less than zero, with a sign opposite to its positive counterpart For Exercises 6-11, match the solution with the problem A. 10001100 B. 10011110 C. 1101010 D. 1100000 E. 1010001 F. 1111000 6. 1110011 + 11001 (binary addition) 7. 1010101 + 10101 (binary addition) 8. 111111111111 (binary addition) For Exercises 12-17. mark the answer true or false as follows: A. True B. False 12 Binary numbers are important in computing because a binary number can be converted into every other base. 13. Binary numbers can be read off in hexadecimal but not in octal. 14. Starting from left to right, every grouping of four binary digits can be read as one hexadecimal digit. 15. A byte is made up of six binary digits 16. Two hexadecimal digits cannot be stored in one byte. 17. Reading octal digits off as binary produces the same result whether read from right to left or from left to right. Exercises 18-47 are problems or short- answer questions. 18. Distinguish between a natural number and a negative number. 19. Distinguish between a natural number and a rational number. 20. Label the following numbers as natural, negative, or rational. a. 1.333333 b. -1/3 c. 1066 d. 2/5 e. 6.2 9. 1111111-111 (binary subtraction) 10.1100111 - 111 (binary subtraction) 11. 1010110 - 101 (binary subtraction) f. (pi)