Test 1 CMSC 2100 Fall 2024

Name ______________________________________

• Please answer each question fully, carefully and thoughtfully.
• No credit will be given for unreadable answers, please write neatly.
• Answer the questions in any order, but please number each answer.
• Make sure that your name is on your test.
• Please show all computations.
  • You may use a calculator, but write down intermediate steps
  • If the purpose of the question is to demonstrate an algorithm or technique and you do not show your computations, the answer will be marked incorrect.

1. Represent the following in the given format
   1. [3 points] -49 in three digit nine's complement.
   2. [3 points] 129 in BCD
   
   
2. The following are encoded as indicated. Represent as signed decimal number.
   1. [3 points] 1001 1010 0011_BCD
   2. [3 points] 1011₂ is in 4 bit two's complement.
   3. [3 points] 1000₂ is in 4 bit two's complement.
   
   
3. [6 points] Signed number representation. Compare and contrast two's complement and binary sign magnitude.

4. [3 points] Describe two advantages the ASCII encoding has over the EBCDIC encoding.
   

5. Gray Code
   1. [4 points] Give a table showing all two bit binary and gray codes, the gray code should align with the binary equivalent.
   2. [2 points] What is the purpose of gray code?
   
   
6. For the expression f(a,b,c) = ac + (b + c)
   1. [4 points] simplify the expression as a sum of products.
   2. [4 points] Provide a truth table for this expression.
   3. [4 points] Provide the canonical sum of products form for this expression.
   4. [4 points] Provide the two different minterm forms for this expression.
   5. [4 points] Provide the two different maxterm forms for this expression.