60-265 Computer Architecture I: Digital Design Winter 2018 Assignment I - Numera
ID: 3876930 • Letter: 6
Question
60-265 Computer Architecture I: Digital Design Winter 2018 Assignment I - Numeracy and Boglean Logic Due: Friday, Jan. 26, 2018 Submit on Blackbaard Representations and Conversions 5 marks] 1. List the binary, octal and hexadecimal numbers from 16 to 31 2 marks] Using a 16-bit representation of unsigned integer values, state and justify what are the maximum permitted values using base-2 (binary) and Binary Coded Decimal (BCD) representations. Explain briefly why the maximum value for BCD is smaller than that for the other representation. 2. [l mark] 3. a) Write the digits for a base 20 system, using an extension of the same digit representation scheme employed for hexadecimal. b) Convert (2014)20 to base 20 c) Convert (BCI.G)2o to base decimal 2 marks] Boolean Logic [5 marks] 4. Prove the identity of each of the following Boolean equations, using algebraic manipulation [2 marks] 5. Given that A. B-0 and A+B-1, use algebraic manipulation to prove that mark] 6. Validate using truth tables: a. Second Distributive law: X+YZ-(XtY) (X+Z) 12 marks]Explanation / Answer
Q1.
Decimal to hexadecimal and octal conversion:
Decimal to binary conversion:
Keep dividing the decimal number by 2 and stores the remainder by adding the remainder after the previous remainder.
Then the binary number representation of the decimal number is the reverse of the number formed by adding remainders.
Example: 49
49/2 gives quotient 24 remainder 1. Number formed by remainder is 1
24/2 gives quotient 12 remainder 0. Number formed by remainder is 10
12/2 gives quotient 6 remainder 0. Number formed by remainder is 100
6/2 gives quotient 3 remainder 0. Number formed by remainder is 1000
3/2 gives quotient 1 remainder 1. Number formed by remainder is 10001
1/2 gives quotient 0 remainder 1. Number formed by remainder is 100011
Finally the number formed by the remainders is 100011.So the reverse of this number is the binary representation of decimal number 49.
(49)10 = (110001)2
So finally hexadecimal,octal and binary representation of 16-31 in decimal is as under:
Decimal Hexadecimal Octal 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 10 9 9 11 10 A 12 11 B 13 12 C 14 13 D 15 14 E 16 15 F 17Related Questions
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