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]