Section 1
Exercises
Distinguish between a natural number and a negative number.
Distinguish between a natural number and a rational number.
Label the following numbers as natural, negative, or rational.a. 1.333333d. $2 / 5$b. " $1 / 3$e. 6.2c. 1066f. $\pi(\mathrm{pi})$
How many ones are there in 891 if it is a number in each of the following bases?a. base 10d. base 13b. base 8e. base 16c. base 12
Express 891 as a polynomial in each of the bases in Exercise 4.
Convert the following numbers from the base shown to base 10 .a. 111 (base 2)d. 777 (base 16)b. 777 (base 8)e. 111 (base 8)c. FEC (base 16)
Explain how base 2 and base 8 are related.
Explain how base 8 and base 16 are related.
Expand the table on page 40 to include the decimal numbers from 11 through 16.
Expand the table in Exercise 9 to include hexadecimal numbers.
Convert the following octal numbers to binary.a. 766d. 142b. 101e. 889c. 202
Convert the following binary numbers to octal.a. 111110110d. 1100010b. 1000001e. 111000111c. 010000010
Convert the following binary numbers to hexadecimal.a. 111110110b. 1000001c. 010000010d. 1100010e. 111000111
Convert the following octal numbers to hexadecimal.a. 777b. 605c. 443d. 521e. 1
Convert the following decimal numbers to octal.a. 901b. 321c. 1492d. 1066c. 2001
Convert the following decimal numbers to binary.a. 45b. 69c. 1066d. 99e. 1
Convert the following decimal numbers to hexadecimal.a. 1066b. 1939c. 1d. 998e. 43
If you were going to represent numbers in base 18 , what symbols might you use to represent the decimal numbers 10 through 17 other than letters?
Convert the following decimal numbers to base 18 using the symbols you suggested in Exercise 18.a. 1066b. 99099c. 1
Perform the following binary additions.a. $1110011+11001$b. $1111111+11111$c. $1010101+10101$
Perform the following octal additions.a. $770+665$b. $101+707$c. $202+667$
Perform the following hexadecimal additions.c. 19AB6 + 43b. $\mathrm{AE} 9+\mathrm{F}$c. $1066+\mathrm{ABCD}$
Perform the following binary subtractions.a. $1100111{ }^{\prime \prime} 111$b. $1010110^{\prime \prime} 101$c. $1111111^{\prime \prime} 111$
. Perform the following octal subtractions.a. $1066^{\prime \prime} 776$b. $1234^{\prime \prime} 765$c. $7766^{\prime \prime} 5544$
Perform the following hexadecimal subtractions.a. ABC " 111b. $9988^{\prime \prime} \mathrm{AB}$c. A9F8 " 1492
Why are binary numbers important in computing?
A byte contains how many bits?
How many bytes are there in one word of a 64 -bit machine?
Why do microprocessors such as pagers have only 8-bit words?
Why is important to study how to manipulate fixed-sized numbers?