CS 266: Computer Architecture I - Homework 4 Solutions - Prof. Mitchell D. Theys, Study notes of Computer Architecture and Organization

Download CS 266: Computer Architecture I - Homework 4 Solutions - Prof. Mitchell D. Theys and more Study notes Computer Architecture and Organization in PDF only on Docsity! University of Illinois at Chicago CS 266: Computer Architecture I Fall 2012 Homework 4 Solutions Question 1 [25 points] Design a combinational circuit that converts a binary number of four bits to a decimal number n BCD. Note that the BCD number is the same as the binary number as long as the input is less than or equal to 9. The binary number from 1010 to 1111 converts into BCD numbers from 1 0000 to 1 0101. Decimal Binary BCD
        0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 2 0 0 1 0 0 0 0 1 0 3 0 0 1 1 0 0 0 1 1 4 0 1 0 0 0 0 1 0 0 5 0 1 0 1 0 0 1 0 1 6 0 1 1 0 0 0 1 1 0 7 0 1 1 1 0 0 1 1 1 8 1 0 0 0 0 1 0 0 0 9 1 0 0 1 0 1 0 0 1 10 1 0 1 0 1 0 0 0 0 11 1 0 1 1 1 0 0 0 1 12 1 1 0 0 1 0 0 1 0 13 1 1 0 1 1 0 0 1 1 14 1 1 1 0 1 0 1 0 0 15 1 1 1 1 1 0 1 0 1 We would like to represent each of  ,  , , ,  as function of  ,  , , , . For each  we build the k-map.  =
 +
  =
̅ AB CD 00 01 1 11 10 1 1 1 00 01 11 10 1 1 AB CD 00 01 1 11 10 00 01 11 10 1  =
̅ +   =
̅ +
̅  =  Therefore we know how to represent a BCD number based on bits from binary representation:  =
 +
  =
̅  =
̅ +   =
̅ +
̅  =  And the circuit is: AB CD 00 01 1 11 10 1 1 1 00 01 11 10 1 1 AB CD 00 01 1 11 10 1 1 1 00 01 11 10 1 1 AB CD 00 01 1 1 11 10 1 1 1 00 01 11 10 1 1 1