Problem Set Answers: Two's Complement

1. Convert the following decimal numbers to 12 bit 2's complement:
   1. 101₁₀ = 0000 0110 0101_2c12
   2. -97₁₀ = 1111 1001 1111_2c12
   3. 620₁₀ = 0010 0110 1100_2c12
   4. -187₁₀ = 1111 0100 0101_2c12
   5. -332₁₀ = 1110 1011 0100_2c12
2. Convert the following 12 bit 2's complement numbers to base 10:
   1. 0000 1011 1011_2c12 = 187₁₀
   2. 1111 1100 0111_2c12 = -57₁₀
   3. 0100 0000 0001_2c12 = 1025₁₀
   4. 1100 0001 1101_2c12 = -995₁₀
   5. 0111 1111 1111_2c12 = 2047₁₀
   6. 1111 1111 1111_2c12 = -1₁₀
   7. 1000 0000 0000_2c12 = -2048₁₀
3. Perform the following additions and subtractions. Assume that all numbers are in 8 bit 2's complement.
   1. 10110101 + 11101011 = 1010 0000
      neg + neg = neg, no overflow
   2. 01100001 + 01010101 = 1011 0110
      pos + pos = neg, overflow
   3. 00010110 + 11010110 = 1110 1100
      pos + neg = neg, no overflow
   4. 00011101 + 01011010 = 0111 0111
      pos + pos = pos, no overflow
   5. 10001111 - 11101101 = 1010 0010
      neg - neg = neg + pos = neg, no overflow
   6. 00101101 - 00011011 = 0001 0010
      pos - pos = pos + neg = pos, no overflow
   7. 00011001 - 11011000 = 0100 0001
      pos - neg = pos + pos = pos, no overflow
   8. 10001110 - 01101010 = 00100100
      neg - pos = neg + neg = pos, overflow
4. Perform the following additions and subtractions. Assume that all numbers are in 32 bit 2's complement. State the sign of each number, the sign of the answer, and whether an overflow occurs.
   1. 00 00 04 C8 + 48 49 B7 6F = 48 49 BC 37
      pos + pos = pos, no overflow
   2. 00 12 5F 89 + 8F DE 27 83 = 8F F0 87 0C
      pos + neg = neg, no overflow
   3. 39 B4 08 75 + 93 19 76 26 = CC CD 7E 9B
      pos + neg = neg, no overflow
   4. 6A 01 B9 33 + 55 62 09 42 = BF 63 C2 75
      pos + pos = neg, overflow
   5. FF FE 59 00 - 23 45 67 89 =
      FF FE 59 00 + DC BA 98 77 = DC B8 F1 77
      neg + neg = neg, no overflow
   6. 49 7B 05 CC - 92 93 8A 6D =
      49 7B 05 CC + 6D 6C 75 93 = B6 E7 7B 5F
      pos + pos = neg, overflow
   7. 86 21 4F BC - 6B A4 59 72 =
      86 21 4F BC + 94 5B A6 8E = 1A 7C F6 4A
      neg + neg = pos, overflow

Email Me | Office Hours | My Home Page | Department Home | MCC Home Page

© Copyright Emmi Schatz 2011