34 CHAPTER 1 / DIGITAL SYSTEMS AND INFORMATION 1-7. "Convert the following binary numbers to decimal: 1001101, 1010011101, and 10101110,1001 1-4. Convert the following decimal numbers to binary: 187, 891.2014. and 20496 1-9. "Convert the following numbers from the given base to the other three bases listed in the table Decimal 369.3125 2 7 Binary ? 10111101.101 ? Octal ? ? 326,5 Hexadecimal ? 2 ? F3CZA 1-10. Convert the following decimal numbers to the indicated bases using the method of Examples 1-4 on page 23 and 1-7 on page 24: () 7562.45 to octal (6) 1938.257 to hexadecimal ( 175.175 to binary 1-11. Perform the following conversion by using base 2 instead of base 10 as the intermediate base for the conversion: (a) (673.6), to hexadecimal (b) (E7C.B), to octal (o) (310.2), to octal 1-12. Perform the following binary multiplications (a) 1010 x 1100 (b) 0110 x 1001 (c) 1111001011101 1-13. Division is composed of multiplications and subtractions Perform the binary division 1010110 + 101 to obtain a quotient and reminder. 1-14. A limited number system uses base 12. There are at most four integer digits The weights of the digits are 12, 12., 12 and 1. Special names are given to the weights as follows: 12 = 1 doren, 12 = 1 gross, and 12 = 1 great gross (a) How many beverage cans are in great gross + 8 gross + 7 dozen + 4? (b) Find the representation in hase 12 for 7569, beverage cans 1-15. Considerable evidence suggests that base 20 has historically been used for number systems in a number of cultures (a) Write the digits for a base 20 system, using an extension of the same digit representation scheme employed for hexadecimal. (b) Convert (2014), to base 20. (e) Convert (BCI G), to decimal. 1-16. "In cach of the following cases, determine the radix r a) (BEE), = (2699), (b) (365), = (194)