University:
Massachusetts Institute of Technology
Course:
16.01 | Unified Engineering I, II, III, & IV
Academic year:

2019
Views:

287

Pages:

4
Author:

anon

C5 Solutions 1. Convert the following base 10 numbers into 8-bit 2’s complement notation 0, -1, -12 To Compute 0 0 = 00000000 To Compute –1 Step 1. Convert 1 to binary 00000001 Step 2. Flip the bits 11111110 Step3. Add 1 11111111 Therefore –1 = 11111111 To Compute –12 Step 1. Convert 12 to binary 00001100 Step 2. Flip the bits 11110011 Step3. Add 1 11110100 Therefore –12 = 11110100 2. Perform each of the following additions assuming that the bit strings represent values in 2’s complement notation. Identify the cases in which the answer is incorrect because of overflow. 1111 1111 11110 + Answer = 11110 Overflow =0 ∴ Answer is correct + 01111 10001 100000 Answer = 00000 Overflow =1 ∴ Answer is incorrect + 01110 01010 11000 Answer = 11000 Overflow =0 ∴ Answer is correct 3. Write an algorithm to convert a negative decimal number into a binary number in 2’s complement form. Assume that the number ranges from +127 to -128 1. If the number is less than 0 a. Multiply by –1 b. Flip the bits by ‘number XOR 0xff’ c. Add 1 to the result 2. Convert the number into binary Hint: You already know how to convert a positive decimal number into binary notation. Think about determining sign and inverting bit positions. 4. Implement your algorithm in Ada95. Turn in an electronic copy of your code listing and a hard copy of your code. GNAT 3.13p (20000509) Copyright 1992-2000 Free Software Foundation, Inc. Compiling: c:/docume~2/jk/desktop/16070/codeso~1/decimal_to_binary.adb (source file time stamp: 200309-17 11:09:18) 1. with Ada.Text_Io; 2. use Ada.Text_Io; 3. 4. with Ada.Integer_Text_Io; 5. use Ada.Integer_Text_Io; 6. 7. procedure Decimal_To_Binary is 8. 9. -- bit-wise operations are only defined for modular types 10. type byte is mod 256; 11. 12. Number_To_Convert : integer; 13. Place_Holder: Byte; 14. 15. Binary_Number : String (1..8); 16. Count : Integer :=8; 17. 18. 19. begin 20. -- set the string to all zeroes 21. Binary_Number :="00000000"; 22. 23. -- get the number to be converted 24. Put("Please enter an integer :"); 25. Get(Number_To_Convert); 26. 27. -- check if the number is negative. If it is, 28. -- convert it into positive 29. if Number_To_Convert < 0 then 30. 31. Number_To_Convert := -1 * Number_To_Convert; 32. 33. -- convert to modular type 34. Place_Holder := Byte'Val(Integer'Pos(Number_To_Convert)); 35. 36. -- flip the bits 37. Place_Holder := Place_Holder xor 2#11111111#; 38. -- add 1 39. Place_Holder := Place_Holder + 2#1#; 40. -- reconvert to integer 41. Number_To_Convert := Integer'Val(Byte'Pos(Place_Holder)); 42. 43. end if; 44. 45. -- decimal to binary conversion 46. -- fill in the bit pattern from left to right 47. loop 48. exit when Count = 0; 49. -- if the remainder is non-zero, the bit is set to 1 50. -- else the bit is 0 51. if (Number_To_Convert mod 2) = 1 then 52. Binary_Number(Count) :='1'; 53. else 54. Binary_Number(Count) :='0'; 55. end if; 56. 57. Count := Count -1; 58. Number_To_Convert := Number_To_Convert/2; 59. 60. end loop; 61. 62. Put(Binary_Number); 63. 64. end Decimal_To_Binary; 65. 66. 67. 67 lines: No errors