Assignment: Hexadecimal and Following Decimal Numbers

Digital Logic Design – CS220 Assignment # 1 Due Date: 11-03-2013 Section V and V3 1. List the first 16 numbers in base 12. Use the alphabets A and B for the last two digits. (4) Base 10 | Base 12 | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 | Last two Digits
10 | A | 11 | B | 12 | 10 | 13 | 11 | 14 | 12 | 15 | 13 |

2. What is the largest binary number that can be obtained by 16 bits? Mention its decimal equivalent. (4)
Largest binary number is (11111111111111111111)2 = (65535)10
Number of bits=n=16
2n-1=216-1=(65535)10
3. Covert the following numbers with indicated bases to decimal: (4310)5 (50)7 (12121)3
(198)12 , ( 1110101.11)2 (4)
(4310)5 = 4x53+3x52+1x51+0x50=(580)10
(50)7 = 5x71+0x70 =(35)10
(12121)3 = 1x34+2x33+1x32+2x31 + 1x30 =(51)10
(198)12 = 1x122+9x121 + 8x120 = (260)10
( 1110101.11)2 = 1x26+1x25+1x22+2x21 + 1x20 =

4. Covert the following decimal numbers to the indicated bases: (4) (a) 7562.45 to octal (b) 1938.257 to hexadecimal (c) 175.175 to binary

5. Convert the hexadecimal number F3A7C2 to binary and octal (2)

6. Add the following numbers without converting to decimal (6) (11010101)2 and (01010111)2 7. Determine the value of the base x if (211)x = (152)8 . (4)

8. Obtain the 1’s and 2’s complement of the following binary numbers: 10101010, 0111000, and 00000.

9. Obtain 9’s and 10’s complement of the following decimal numbers: 13579, 90090 and 00000.

10. Find the 10’ complement of (935)11.

11. Perform the subtraction with the following decimal numbers using (1) 10’s complement and (2) 9’s complement. Check your answer by straight subtraction.

a. 5250 – 321 b. 20 – 1000

12. Perform the subtraction with the following decimal numbers using (1) 2’s complement and (2) 1’s complement. Check your answer by straight subtraction.

c. 11010 – 1101 d. 100 - 110000

13. Represent decimal number 8620 in BCD and as a binary number. (4)

14. Assign a binary code in some orderly manner to the 52 playing cards. Use the minimum number of bits. (4)

15. List the ten BCD digits with an even parity in the leftmost position. (Total of five bits per digit). Repeat with an odd parity bit. (4)

16. Write your full name in ASCII using an eight bit code with the leftmost bit always 0. Include a space between names and a period after middle initial. (4)

17. Decode the following ASCII code : (4 )

18. Show the bit configuration that represents the decimal numbers 295 (a) in binary, (b) in BCD, and (c) in ASCII (4)

19. “Schoolhouse Rock’ had a song called ‘Little Twelvetoes’ which had an alien character with 6 fingers on each hand who could count by 12 as easily as we count by 10. If he counted to 100 in his base 12 (duodecimal), what would that be in decimal? (5)

20. Fill out the following table: (15)

Decimal | Binary | Octal | Hexadecimal | 1 | | | | 2 | | | | 3 | | | | 4 | | | | 5 | | | | 6 | | | | 7 | | | | 8 | | | | 9 | | | | 10 | | | | 11 | | | | 12 | | | | 13 | | | | 14 | | | | 15 | | | | 16 | | | | 17 | | | | 18 | | | | 19 | | | | 20 | | | |