Signed eight-bit values

1. Treat 10000000 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 0.
6. Add those contributions: -128 + 0 = -128.
7. As an unsigned pattern, the same eight bits represent 128.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000000.
11. Answer: signed(10000000) = -128.

Final answer: -128

1. Treat 10000001 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 1.
6. Add those contributions: -128 + 1 = -127.
7. As an unsigned pattern, the same eight bits represent 129.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111111.
11. Answer: signed(10000001) = -127.

Final answer: -127

1. Treat 10000010 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 2.
6. Add those contributions: -128 + 2 = -126.
7. As an unsigned pattern, the same eight bits represent 130.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111110.
11. Answer: signed(10000010) = -126.

Final answer: -126

1. Treat 10000011 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 3.
6. Add those contributions: -128 + 3 = -125.
7. As an unsigned pattern, the same eight bits represent 131.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111101.
11. Answer: signed(10000011) = -125.

Final answer: -125

1. Treat 10000100 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 4.
6. Add those contributions: -128 + 4 = -124.
7. As an unsigned pattern, the same eight bits represent 132.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111100.
11. Answer: signed(10000100) = -124.

Final answer: -124

1. Treat 10000101 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 5.
6. Add those contributions: -128 + 5 = -123.
7. As an unsigned pattern, the same eight bits represent 133.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111011.
11. Answer: signed(10000101) = -123.

Final answer: -123

1. Treat 10000110 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 6.
6. Add those contributions: -128 + 6 = -122.
7. As an unsigned pattern, the same eight bits represent 134.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111010.
11. Answer: signed(10000110) = -122.

Final answer: -122

1. Treat 10000111 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 7.
6. Add those contributions: -128 + 7 = -121.
7. As an unsigned pattern, the same eight bits represent 135.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01111000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111001.
11. Answer: signed(10000111) = -121.

Final answer: -121

1. Treat 10001000 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 8.
6. Add those contributions: -128 + 8 = -120.
7. As an unsigned pattern, the same eight bits represent 136.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01111000.
11. Answer: signed(10001000) = -120.

Final answer: -120

1. Treat 10001001 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 9.
6. Add those contributions: -128 + 9 = -119.
7. As an unsigned pattern, the same eight bits represent 137.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110111.
11. Answer: signed(10001001) = -119.

Final answer: -119

1. Treat 10001010 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 10.
6. Add those contributions: -128 + 10 = -118.
7. As an unsigned pattern, the same eight bits represent 138.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110110.
11. Answer: signed(10001010) = -118.

Final answer: -118

1. Treat 10001011 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 11.
6. Add those contributions: -128 + 11 = -117.
7. As an unsigned pattern, the same eight bits represent 139.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110101.
11. Answer: signed(10001011) = -117.

Final answer: -117

1. Treat 10001100 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 12.
6. Add those contributions: -128 + 12 = -116.
7. As an unsigned pattern, the same eight bits represent 140.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110100.
11. Answer: signed(10001100) = -116.

Final answer: -116

1. Treat 10001101 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 13.
6. Add those contributions: -128 + 13 = -115.
7. As an unsigned pattern, the same eight bits represent 141.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110011.
11. Answer: signed(10001101) = -115.

Final answer: -115

1. Treat 10001110 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 14.
6. Add those contributions: -128 + 14 = -114.
7. As an unsigned pattern, the same eight bits represent 142.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110010.
11. Answer: signed(10001110) = -114.

Final answer: -114

1. Treat 10001111 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 15.
6. Add those contributions: -128 + 15 = -113.
7. As an unsigned pattern, the same eight bits represent 143.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01110000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110001.
11. Answer: signed(10001111) = -113.

Final answer: -113

1. Treat 10010000 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 16.
6. Add those contributions: -128 + 16 = -112.
7. As an unsigned pattern, the same eight bits represent 144.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01110000.
11. Answer: signed(10010000) = -112.

Final answer: -112

1. Treat 10010001 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 17.
6. Add those contributions: -128 + 17 = -111.
7. As an unsigned pattern, the same eight bits represent 145.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101111.
11. Answer: signed(10010001) = -111.

Final answer: -111

1. Treat 10010010 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 18.
6. Add those contributions: -128 + 18 = -110.
7. As an unsigned pattern, the same eight bits represent 146.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101110.
11. Answer: signed(10010010) = -110.

Final answer: -110

1. Treat 10010011 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 19.
6. Add those contributions: -128 + 19 = -109.
7. As an unsigned pattern, the same eight bits represent 147.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101101.
11. Answer: signed(10010011) = -109.

Final answer: -109

1. Treat 10010100 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 20.
6. Add those contributions: -128 + 20 = -108.
7. As an unsigned pattern, the same eight bits represent 148.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101100.
11. Answer: signed(10010100) = -108.

Final answer: -108

1. Treat 10010101 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 21.
6. Add those contributions: -128 + 21 = -107.
7. As an unsigned pattern, the same eight bits represent 149.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101011.
11. Answer: signed(10010101) = -107.

Final answer: -107

1. Treat 10010110 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 22.
6. Add those contributions: -128 + 22 = -106.
7. As an unsigned pattern, the same eight bits represent 150.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101010.
11. Answer: signed(10010110) = -106.

Final answer: -106

1. Treat 10010111 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 23.
6. Add those contributions: -128 + 23 = -105.
7. As an unsigned pattern, the same eight bits represent 151.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01101000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101001.
11. Answer: signed(10010111) = -105.

Final answer: -105

1. Treat 10011000 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 24.
6. Add those contributions: -128 + 24 = -104.
7. As an unsigned pattern, the same eight bits represent 152.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01101000.
11. Answer: signed(10011000) = -104.

Final answer: -104

1. Treat 10011001 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 25.
6. Add those contributions: -128 + 25 = -103.
7. As an unsigned pattern, the same eight bits represent 153.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100111.
11. Answer: signed(10011001) = -103.

Final answer: -103

1. Treat 10011010 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 26.
6. Add those contributions: -128 + 26 = -102.
7. As an unsigned pattern, the same eight bits represent 154.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100110.
11. Answer: signed(10011010) = -102.

Final answer: -102

1. Treat 10011011 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 27.
6. Add those contributions: -128 + 27 = -101.
7. As an unsigned pattern, the same eight bits represent 155.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100101.
11. Answer: signed(10011011) = -101.

Final answer: -101

1. Treat 10011100 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 28.
6. Add those contributions: -128 + 28 = -100.
7. As an unsigned pattern, the same eight bits represent 156.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100100.
11. Answer: signed(10011100) = -100.

Final answer: -100

1. Treat 10011101 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 29.
6. Add those contributions: -128 + 29 = -99.
7. As an unsigned pattern, the same eight bits represent 157.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100011.
11. Answer: signed(10011101) = -99.

Final answer: -99

1. Treat 10011110 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 30.
6. Add those contributions: -128 + 30 = -98.
7. As an unsigned pattern, the same eight bits represent 158.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100010.
11. Answer: signed(10011110) = -98.

Final answer: -98

1. Treat 10011111 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 31.
6. Add those contributions: -128 + 31 = -97.
7. As an unsigned pattern, the same eight bits represent 159.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 01100000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 01100001.
11. Answer: signed(10011111) = -97.

Final answer: -97