Signed eight-bit values

1. Treat 01000000 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 64.
6. Add those contributions: 0 + 64 = 64.
7. As an unsigned pattern, the same eight bits represent 64.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000000.
11. Answer: signed(01000000) = 64.

Final answer: 64

1. Treat 01000001 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 65.
6. Add those contributions: 0 + 65 = 65.
7. As an unsigned pattern, the same eight bits represent 65.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111111.
11. Answer: signed(01000001) = 65.

Final answer: 65

1. Treat 01000010 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 66.
6. Add those contributions: 0 + 66 = 66.
7. As an unsigned pattern, the same eight bits represent 66.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111110.
11. Answer: signed(01000010) = 66.

Final answer: 66

1. Treat 01000011 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 67.
6. Add those contributions: 0 + 67 = 67.
7. As an unsigned pattern, the same eight bits represent 67.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111101.
11. Answer: signed(01000011) = 67.

Final answer: 67

1. Treat 01000100 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 68.
6. Add those contributions: 0 + 68 = 68.
7. As an unsigned pattern, the same eight bits represent 68.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111100.
11. Answer: signed(01000100) = 68.

Final answer: 68

1. Treat 01000101 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 69.
6. Add those contributions: 0 + 69 = 69.
7. As an unsigned pattern, the same eight bits represent 69.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111011.
11. Answer: signed(01000101) = 69.

Final answer: 69

1. Treat 01000110 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 70.
6. Add those contributions: 0 + 70 = 70.
7. As an unsigned pattern, the same eight bits represent 70.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111010.
11. Answer: signed(01000110) = 70.

Final answer: 70

1. Treat 01000111 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 71.
6. Add those contributions: 0 + 71 = 71.
7. As an unsigned pattern, the same eight bits represent 71.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10111000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111001.
11. Answer: signed(01000111) = 71.

Final answer: 71

1. Treat 01001000 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 72.
6. Add those contributions: 0 + 72 = 72.
7. As an unsigned pattern, the same eight bits represent 72.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10111000.
11. Answer: signed(01001000) = 72.

Final answer: 72

1. Treat 01001001 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 73.
6. Add those contributions: 0 + 73 = 73.
7. As an unsigned pattern, the same eight bits represent 73.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110111.
11. Answer: signed(01001001) = 73.

Final answer: 73

1. Treat 01001010 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 74.
6. Add those contributions: 0 + 74 = 74.
7. As an unsigned pattern, the same eight bits represent 74.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110110.
11. Answer: signed(01001010) = 74.

Final answer: 74

1. Treat 01001011 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 75.
6. Add those contributions: 0 + 75 = 75.
7. As an unsigned pattern, the same eight bits represent 75.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110101.
11. Answer: signed(01001011) = 75.

Final answer: 75

1. Treat 01001100 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 76.
6. Add those contributions: 0 + 76 = 76.
7. As an unsigned pattern, the same eight bits represent 76.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110100.
11. Answer: signed(01001100) = 76.

Final answer: 76

1. Treat 01001101 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 77.
6. Add those contributions: 0 + 77 = 77.
7. As an unsigned pattern, the same eight bits represent 77.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110011.
11. Answer: signed(01001101) = 77.

Final answer: 77

1. Treat 01001110 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 78.
6. Add those contributions: 0 + 78 = 78.
7. As an unsigned pattern, the same eight bits represent 78.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110010.
11. Answer: signed(01001110) = 78.

Final answer: 78

1. Treat 01001111 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 79.
6. Add those contributions: 0 + 79 = 79.
7. As an unsigned pattern, the same eight bits represent 79.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10110000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110001.
11. Answer: signed(01001111) = 79.

Final answer: 79

1. Treat 01010000 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 80.
6. Add those contributions: 0 + 80 = 80.
7. As an unsigned pattern, the same eight bits represent 80.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10110000.
11. Answer: signed(01010000) = 80.

Final answer: 80

1. Treat 01010001 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 81.
6. Add those contributions: 0 + 81 = 81.
7. As an unsigned pattern, the same eight bits represent 81.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101111.
11. Answer: signed(01010001) = 81.

Final answer: 81

1. Treat 01010010 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 82.
6. Add those contributions: 0 + 82 = 82.
7. As an unsigned pattern, the same eight bits represent 82.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101110.
11. Answer: signed(01010010) = 82.

Final answer: 82

1. Treat 01010011 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 83.
6. Add those contributions: 0 + 83 = 83.
7. As an unsigned pattern, the same eight bits represent 83.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101101.
11. Answer: signed(01010011) = 83.

Final answer: 83

1. Treat 01010100 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 84.
6. Add those contributions: 0 + 84 = 84.
7. As an unsigned pattern, the same eight bits represent 84.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101100.
11. Answer: signed(01010100) = 84.

Final answer: 84

1. Treat 01010101 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 85.
6. Add those contributions: 0 + 85 = 85.
7. As an unsigned pattern, the same eight bits represent 85.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101011.
11. Answer: signed(01010101) = 85.

Final answer: 85

1. Treat 01010110 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 86.
6. Add those contributions: 0 + 86 = 86.
7. As an unsigned pattern, the same eight bits represent 86.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101010.
11. Answer: signed(01010110) = 86.

Final answer: 86

1. Treat 01010111 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 87.
6. Add those contributions: 0 + 87 = 87.
7. As an unsigned pattern, the same eight bits represent 87.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10101000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101001.
11. Answer: signed(01010111) = 87.

Final answer: 87

1. Treat 01011000 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 88.
6. Add those contributions: 0 + 88 = 88.
7. As an unsigned pattern, the same eight bits represent 88.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10101000.
11. Answer: signed(01011000) = 88.

Final answer: 88

1. Treat 01011001 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 89.
6. Add those contributions: 0 + 89 = 89.
7. As an unsigned pattern, the same eight bits represent 89.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100111.
11. Answer: signed(01011001) = 89.

Final answer: 89

1. Treat 01011010 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 90.
6. Add those contributions: 0 + 90 = 90.
7. As an unsigned pattern, the same eight bits represent 90.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100110.
11. Answer: signed(01011010) = 90.

Final answer: 90

1. Treat 01011011 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 91.
6. Add those contributions: 0 + 91 = 91.
7. As an unsigned pattern, the same eight bits represent 91.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100101.
11. Answer: signed(01011011) = 91.

Final answer: 91

1. Treat 01011100 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 92.
6. Add those contributions: 0 + 92 = 92.
7. As an unsigned pattern, the same eight bits represent 92.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100100.
11. Answer: signed(01011100) = 92.

Final answer: 92

1. Treat 01011101 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 93.
6. Add those contributions: 0 + 93 = 93.
7. As an unsigned pattern, the same eight bits represent 93.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100011.
11. Answer: signed(01011101) = 93.

Final answer: 93

1. Treat 01011110 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 94.
6. Add those contributions: 0 + 94 = 94.
7. As an unsigned pattern, the same eight bits represent 94.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100010.
11. Answer: signed(01011110) = 94.

Final answer: 94

1. Treat 01011111 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 0, so its signed contribution is 0.
5. The lower seven bits contribute 95.
6. Add those contributions: 0 + 95 = 95.
7. As an unsigned pattern, the same eight bits represent 95.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10100000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100001.
11. Answer: signed(01011111) = 95.

Final answer: 95