Signed eight-bit values

1. Treat 11000000 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 64.
6. Add those contributions: -128 + 64 = -64.
7. As an unsigned pattern, the same eight bits represent 192.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000000.
11. Answer: signed(11000000) = -64.

Final answer: -64

1. Treat 11000001 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 65.
6. Add those contributions: -128 + 65 = -63.
7. As an unsigned pattern, the same eight bits represent 193.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111111.
11. Answer: signed(11000001) = -63.

Final answer: -63

1. Treat 11000010 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 66.
6. Add those contributions: -128 + 66 = -62.
7. As an unsigned pattern, the same eight bits represent 194.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111110.
11. Answer: signed(11000010) = -62.

Final answer: -62

1. Treat 11000011 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 67.
6. Add those contributions: -128 + 67 = -61.
7. As an unsigned pattern, the same eight bits represent 195.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111101.
11. Answer: signed(11000011) = -61.

Final answer: -61

1. Treat 11000100 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 68.
6. Add those contributions: -128 + 68 = -60.
7. As an unsigned pattern, the same eight bits represent 196.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111100.
11. Answer: signed(11000100) = -60.

Final answer: -60

1. Treat 11000101 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 69.
6. Add those contributions: -128 + 69 = -59.
7. As an unsigned pattern, the same eight bits represent 197.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111011.
11. Answer: signed(11000101) = -59.

Final answer: -59

1. Treat 11000110 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 70.
6. Add those contributions: -128 + 70 = -58.
7. As an unsigned pattern, the same eight bits represent 198.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111010.
11. Answer: signed(11000110) = -58.

Final answer: -58

1. Treat 11000111 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 71.
6. Add those contributions: -128 + 71 = -57.
7. As an unsigned pattern, the same eight bits represent 199.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00111000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111001.
11. Answer: signed(11000111) = -57.

Final answer: -57

1. Treat 11001000 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 72.
6. Add those contributions: -128 + 72 = -56.
7. As an unsigned pattern, the same eight bits represent 200.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00111000.
11. Answer: signed(11001000) = -56.

Final answer: -56

1. Treat 11001001 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 73.
6. Add those contributions: -128 + 73 = -55.
7. As an unsigned pattern, the same eight bits represent 201.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110111.
11. Answer: signed(11001001) = -55.

Final answer: -55

1. Treat 11001010 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 74.
6. Add those contributions: -128 + 74 = -54.
7. As an unsigned pattern, the same eight bits represent 202.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110110.
11. Answer: signed(11001010) = -54.

Final answer: -54

1. Treat 11001011 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 75.
6. Add those contributions: -128 + 75 = -53.
7. As an unsigned pattern, the same eight bits represent 203.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110101.
11. Answer: signed(11001011) = -53.

Final answer: -53

1. Treat 11001100 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 76.
6. Add those contributions: -128 + 76 = -52.
7. As an unsigned pattern, the same eight bits represent 204.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110100.
11. Answer: signed(11001100) = -52.

Final answer: -52

1. Treat 11001101 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 77.
6. Add those contributions: -128 + 77 = -51.
7. As an unsigned pattern, the same eight bits represent 205.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110011.
11. Answer: signed(11001101) = -51.

Final answer: -51

1. Treat 11001110 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 78.
6. Add those contributions: -128 + 78 = -50.
7. As an unsigned pattern, the same eight bits represent 206.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110010.
11. Answer: signed(11001110) = -50.

Final answer: -50

1. Treat 11001111 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 79.
6. Add those contributions: -128 + 79 = -49.
7. As an unsigned pattern, the same eight bits represent 207.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00110000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110001.
11. Answer: signed(11001111) = -49.

Final answer: -49

1. Treat 11010000 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 80.
6. Add those contributions: -128 + 80 = -48.
7. As an unsigned pattern, the same eight bits represent 208.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00110000.
11. Answer: signed(11010000) = -48.

Final answer: -48

1. Treat 11010001 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 81.
6. Add those contributions: -128 + 81 = -47.
7. As an unsigned pattern, the same eight bits represent 209.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101111.
11. Answer: signed(11010001) = -47.

Final answer: -47

1. Treat 11010010 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 82.
6. Add those contributions: -128 + 82 = -46.
7. As an unsigned pattern, the same eight bits represent 210.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101110.
11. Answer: signed(11010010) = -46.

Final answer: -46

1. Treat 11010011 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 83.
6. Add those contributions: -128 + 83 = -45.
7. As an unsigned pattern, the same eight bits represent 211.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101101.
11. Answer: signed(11010011) = -45.

Final answer: -45

1. Treat 11010100 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 84.
6. Add those contributions: -128 + 84 = -44.
7. As an unsigned pattern, the same eight bits represent 212.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101100.
11. Answer: signed(11010100) = -44.

Final answer: -44

1. Treat 11010101 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 85.
6. Add those contributions: -128 + 85 = -43.
7. As an unsigned pattern, the same eight bits represent 213.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101011.
11. Answer: signed(11010101) = -43.

Final answer: -43

1. Treat 11010110 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 86.
6. Add those contributions: -128 + 86 = -42.
7. As an unsigned pattern, the same eight bits represent 214.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101010.
11. Answer: signed(11010110) = -42.

Final answer: -42

1. Treat 11010111 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 87.
6. Add those contributions: -128 + 87 = -41.
7. As an unsigned pattern, the same eight bits represent 215.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00101000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101001.
11. Answer: signed(11010111) = -41.

Final answer: -41

1. Treat 11011000 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 88.
6. Add those contributions: -128 + 88 = -40.
7. As an unsigned pattern, the same eight bits represent 216.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00101000.
11. Answer: signed(11011000) = -40.

Final answer: -40

1. Treat 11011001 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 89.
6. Add those contributions: -128 + 89 = -39.
7. As an unsigned pattern, the same eight bits represent 217.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100111.
11. Answer: signed(11011001) = -39.

Final answer: -39

1. Treat 11011010 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 90.
6. Add those contributions: -128 + 90 = -38.
7. As an unsigned pattern, the same eight bits represent 218.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100110.
11. Answer: signed(11011010) = -38.

Final answer: -38

1. Treat 11011011 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 91.
6. Add those contributions: -128 + 91 = -37.
7. As an unsigned pattern, the same eight bits represent 219.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100101.
11. Answer: signed(11011011) = -37.

Final answer: -37

1. Treat 11011100 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 92.
6. Add those contributions: -128 + 92 = -36.
7. As an unsigned pattern, the same eight bits represent 220.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100100.
11. Answer: signed(11011100) = -36.

Final answer: -36

1. Treat 11011101 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 93.
6. Add those contributions: -128 + 93 = -35.
7. As an unsigned pattern, the same eight bits represent 221.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100011.
11. Answer: signed(11011101) = -35.

Final answer: -35

1. Treat 11011110 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 94.
6. Add those contributions: -128 + 94 = -34.
7. As an unsigned pattern, the same eight bits represent 222.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100010.
11. Answer: signed(11011110) = -34.

Final answer: -34

1. Treat 11011111 as exactly eight bits.
2. For signed 8-bit values the leftmost column has weight −128, not +128.
3. The remaining seven columns have weights 64, 32, 16, 8, 4, 2 and 1.
4. The leading sign bit is 1, so its signed contribution is -128.
5. The lower seven bits contribute 95.
6. Add those contributions: -128 + 95 = -33.
7. As an unsigned pattern, the same eight bits represent 223.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00100000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100001.
11. Answer: signed(11011111) = -33.

Final answer: -33