Signed eight-bit values

1. Treat 10100000 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 32.
6. Add those contributions: -128 + 32 = -96.
7. As an unsigned pattern, the same eight bits represent 160.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100000.
11. Answer: signed(10100000) = -96.

Final answer: -96

1. Treat 10100001 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 33.
6. Add those contributions: -128 + 33 = -95.
7. As an unsigned pattern, the same eight bits represent 161.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011111.
11. Answer: signed(10100001) = -95.

Final answer: -95

1. Treat 10100010 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 34.
6. Add those contributions: -128 + 34 = -94.
7. As an unsigned pattern, the same eight bits represent 162.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011110.
11. Answer: signed(10100010) = -94.

Final answer: -94

1. Treat 10100011 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 35.
6. Add those contributions: -128 + 35 = -93.
7. As an unsigned pattern, the same eight bits represent 163.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011101.
11. Answer: signed(10100011) = -93.

Final answer: -93

1. Treat 10100100 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 36.
6. Add those contributions: -128 + 36 = -92.
7. As an unsigned pattern, the same eight bits represent 164.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011100.
11. Answer: signed(10100100) = -92.

Final answer: -92

1. Treat 10100101 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 37.
6. Add those contributions: -128 + 37 = -91.
7. As an unsigned pattern, the same eight bits represent 165.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011011.
11. Answer: signed(10100101) = -91.

Final answer: -91

1. Treat 10100110 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 38.
6. Add those contributions: -128 + 38 = -90.
7. As an unsigned pattern, the same eight bits represent 166.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011010.
11. Answer: signed(10100110) = -90.

Final answer: -90

1. Treat 10100111 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 39.
6. Add those contributions: -128 + 39 = -89.
7. As an unsigned pattern, the same eight bits represent 167.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01011000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011001.
11. Answer: signed(10100111) = -89.

Final answer: -89

1. Treat 10101000 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 40.
6. Add those contributions: -128 + 40 = -88.
7. As an unsigned pattern, the same eight bits represent 168.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01011000.
11. Answer: signed(10101000) = -88.

Final answer: -88

1. Treat 10101001 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 41.
6. Add those contributions: -128 + 41 = -87.
7. As an unsigned pattern, the same eight bits represent 169.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010111.
11. Answer: signed(10101001) = -87.

Final answer: -87

1. Treat 10101010 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 42.
6. Add those contributions: -128 + 42 = -86.
7. As an unsigned pattern, the same eight bits represent 170.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010110.
11. Answer: signed(10101010) = -86.

Final answer: -86

1. Treat 10101011 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 43.
6. Add those contributions: -128 + 43 = -85.
7. As an unsigned pattern, the same eight bits represent 171.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010101.
11. Answer: signed(10101011) = -85.

Final answer: -85

1. Treat 10101100 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 44.
6. Add those contributions: -128 + 44 = -84.
7. As an unsigned pattern, the same eight bits represent 172.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010100.
11. Answer: signed(10101100) = -84.

Final answer: -84

1. Treat 10101101 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 45.
6. Add those contributions: -128 + 45 = -83.
7. As an unsigned pattern, the same eight bits represent 173.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010011.
11. Answer: signed(10101101) = -83.

Final answer: -83

1. Treat 10101110 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 46.
6. Add those contributions: -128 + 46 = -82.
7. As an unsigned pattern, the same eight bits represent 174.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010010.
11. Answer: signed(10101110) = -82.

Final answer: -82

1. Treat 10101111 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 47.
6. Add those contributions: -128 + 47 = -81.
7. As an unsigned pattern, the same eight bits represent 175.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01010000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010001.
11. Answer: signed(10101111) = -81.

Final answer: -81

1. Treat 10110000 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 48.
6. Add those contributions: -128 + 48 = -80.
7. As an unsigned pattern, the same eight bits represent 176.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01010000.
11. Answer: signed(10110000) = -80.

Final answer: -80

1. Treat 10110001 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 49.
6. Add those contributions: -128 + 49 = -79.
7. As an unsigned pattern, the same eight bits represent 177.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001111.
11. Answer: signed(10110001) = -79.

Final answer: -79

1. Treat 10110010 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 50.
6. Add those contributions: -128 + 50 = -78.
7. As an unsigned pattern, the same eight bits represent 178.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001110.
11. Answer: signed(10110010) = -78.

Final answer: -78

1. Treat 10110011 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 51.
6. Add those contributions: -128 + 51 = -77.
7. As an unsigned pattern, the same eight bits represent 179.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001101.
11. Answer: signed(10110011) = -77.

Final answer: -77

1. Treat 10110100 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 52.
6. Add those contributions: -128 + 52 = -76.
7. As an unsigned pattern, the same eight bits represent 180.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001100.
11. Answer: signed(10110100) = -76.

Final answer: -76

1. Treat 10110101 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 53.
6. Add those contributions: -128 + 53 = -75.
7. As an unsigned pattern, the same eight bits represent 181.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001011.
11. Answer: signed(10110101) = -75.

Final answer: -75

1. Treat 10110110 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 54.
6. Add those contributions: -128 + 54 = -74.
7. As an unsigned pattern, the same eight bits represent 182.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001010.
11. Answer: signed(10110110) = -74.

Final answer: -74

1. Treat 10110111 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 55.
6. Add those contributions: -128 + 55 = -73.
7. As an unsigned pattern, the same eight bits represent 183.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01001000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001001.
11. Answer: signed(10110111) = -73.

Final answer: -73

1. Treat 10111000 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 56.
6. Add those contributions: -128 + 56 = -72.
7. As an unsigned pattern, the same eight bits represent 184.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01001000.
11. Answer: signed(10111000) = -72.

Final answer: -72

1. Treat 10111001 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 57.
6. Add those contributions: -128 + 57 = -71.
7. As an unsigned pattern, the same eight bits represent 185.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000111.
11. Answer: signed(10111001) = -71.

Final answer: -71

1. Treat 10111010 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 58.
6. Add those contributions: -128 + 58 = -70.
7. As an unsigned pattern, the same eight bits represent 186.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000110.
11. Answer: signed(10111010) = -70.

Final answer: -70

1. Treat 10111011 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 59.
6. Add those contributions: -128 + 59 = -69.
7. As an unsigned pattern, the same eight bits represent 187.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000101.
11. Answer: signed(10111011) = -69.

Final answer: -69

1. Treat 10111100 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 60.
6. Add those contributions: -128 + 60 = -68.
7. As an unsigned pattern, the same eight bits represent 188.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000100.
11. Answer: signed(10111100) = -68.

Final answer: -68

1. Treat 10111101 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 61.
6. Add those contributions: -128 + 61 = -67.
7. As an unsigned pattern, the same eight bits represent 189.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000011.
11. Answer: signed(10111101) = -67.

Final answer: -67

1. Treat 10111110 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 62.
6. Add those contributions: -128 + 62 = -66.
7. As an unsigned pattern, the same eight bits represent 190.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000010.
11. Answer: signed(10111110) = -66.

Final answer: -66

1. Treat 10111111 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 63.
6. Add those contributions: -128 + 63 = -65.
7. As an unsigned pattern, the same eight bits represent 191.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01000000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01000001.
11. Answer: signed(10111111) = -65.

Final answer: -65