Assignment: Hexadecimal and Following Decimal Numbers

Topics: Hexadecimal, Binary numeral system, Decimal Pages: 4 (536 words) Published: June 21, 2013
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...
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