Signed eight-bit values

1. Treat 00100000 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 32.
6. Add those contributions: 0 + 32 = 32.
7. As an unsigned pattern, the same eight bits represent 32.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100000.
11. Answer: signed(00100000) = 32.

Final answer: 32

1. Treat 00100001 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 33.
6. Add those contributions: 0 + 33 = 33.
7. As an unsigned pattern, the same eight bits represent 33.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011111.
11. Answer: signed(00100001) = 33.

Final answer: 33

1. Treat 00100010 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 34.
6. Add those contributions: 0 + 34 = 34.
7. As an unsigned pattern, the same eight bits represent 34.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011110.
11. Answer: signed(00100010) = 34.

Final answer: 34

1. Treat 00100011 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 35.
6. Add those contributions: 0 + 35 = 35.
7. As an unsigned pattern, the same eight bits represent 35.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011101.
11. Answer: signed(00100011) = 35.

Final answer: 35

1. Treat 00100100 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 36.
6. Add those contributions: 0 + 36 = 36.
7. As an unsigned pattern, the same eight bits represent 36.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011100.
11. Answer: signed(00100100) = 36.

Final answer: 36

1. Treat 00100101 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 37.
6. Add those contributions: 0 + 37 = 37.
7. As an unsigned pattern, the same eight bits represent 37.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011011.
11. Answer: signed(00100101) = 37.

Final answer: 37

1. Treat 00100110 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 38.
6. Add those contributions: 0 + 38 = 38.
7. As an unsigned pattern, the same eight bits represent 38.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011010.
11. Answer: signed(00100110) = 38.

Final answer: 38

1. Treat 00100111 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 39.
6. Add those contributions: 0 + 39 = 39.
7. As an unsigned pattern, the same eight bits represent 39.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11011000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011001.
11. Answer: signed(00100111) = 39.

Final answer: 39

1. Treat 00101000 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 40.
6. Add those contributions: 0 + 40 = 40.
7. As an unsigned pattern, the same eight bits represent 40.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11011000.
11. Answer: signed(00101000) = 40.

Final answer: 40

1. Treat 00101001 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 41.
6. Add those contributions: 0 + 41 = 41.
7. As an unsigned pattern, the same eight bits represent 41.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010111.
11. Answer: signed(00101001) = 41.

Final answer: 41

1. Treat 00101010 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 42.
6. Add those contributions: 0 + 42 = 42.
7. As an unsigned pattern, the same eight bits represent 42.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010110.
11. Answer: signed(00101010) = 42.

Final answer: 42

1. Treat 00101011 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 43.
6. Add those contributions: 0 + 43 = 43.
7. As an unsigned pattern, the same eight bits represent 43.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010101.
11. Answer: signed(00101011) = 43.

Final answer: 43

1. Treat 00101100 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 44.
6. Add those contributions: 0 + 44 = 44.
7. As an unsigned pattern, the same eight bits represent 44.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010100.
11. Answer: signed(00101100) = 44.

Final answer: 44

1. Treat 00101101 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 45.
6. Add those contributions: 0 + 45 = 45.
7. As an unsigned pattern, the same eight bits represent 45.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010011.
11. Answer: signed(00101101) = 45.

Final answer: 45

1. Treat 00101110 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 46.
6. Add those contributions: 0 + 46 = 46.
7. As an unsigned pattern, the same eight bits represent 46.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010010.
11. Answer: signed(00101110) = 46.

Final answer: 46

1. Treat 00101111 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 47.
6. Add those contributions: 0 + 47 = 47.
7. As an unsigned pattern, the same eight bits represent 47.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11010000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010001.
11. Answer: signed(00101111) = 47.

Final answer: 47

1. Treat 00110000 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 48.
6. Add those contributions: 0 + 48 = 48.
7. As an unsigned pattern, the same eight bits represent 48.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11010000.
11. Answer: signed(00110000) = 48.

Final answer: 48

1. Treat 00110001 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 49.
6. Add those contributions: 0 + 49 = 49.
7. As an unsigned pattern, the same eight bits represent 49.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001111.
11. Answer: signed(00110001) = 49.

Final answer: 49

1. Treat 00110010 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 50.
6. Add those contributions: 0 + 50 = 50.
7. As an unsigned pattern, the same eight bits represent 50.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001110.
11. Answer: signed(00110010) = 50.

Final answer: 50

1. Treat 00110011 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 51.
6. Add those contributions: 0 + 51 = 51.
7. As an unsigned pattern, the same eight bits represent 51.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001101.
11. Answer: signed(00110011) = 51.

Final answer: 51

1. Treat 00110100 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 52.
6. Add those contributions: 0 + 52 = 52.
7. As an unsigned pattern, the same eight bits represent 52.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001100.
11. Answer: signed(00110100) = 52.

Final answer: 52

1. Treat 00110101 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 53.
6. Add those contributions: 0 + 53 = 53.
7. As an unsigned pattern, the same eight bits represent 53.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001011.
11. Answer: signed(00110101) = 53.

Final answer: 53

1. Treat 00110110 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 54.
6. Add those contributions: 0 + 54 = 54.
7. As an unsigned pattern, the same eight bits represent 54.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001010.
11. Answer: signed(00110110) = 54.

Final answer: 54

1. Treat 00110111 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 55.
6. Add those contributions: 0 + 55 = 55.
7. As an unsigned pattern, the same eight bits represent 55.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11001000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001001.
11. Answer: signed(00110111) = 55.

Final answer: 55

1. Treat 00111000 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 56.
6. Add those contributions: 0 + 56 = 56.
7. As an unsigned pattern, the same eight bits represent 56.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11001000.
11. Answer: signed(00111000) = 56.

Final answer: 56

1. Treat 00111001 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 57.
6. Add those contributions: 0 + 57 = 57.
7. As an unsigned pattern, the same eight bits represent 57.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000111.
11. Answer: signed(00111001) = 57.

Final answer: 57

1. Treat 00111010 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 58.
6. Add those contributions: 0 + 58 = 58.
7. As an unsigned pattern, the same eight bits represent 58.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000110.
11. Answer: signed(00111010) = 58.

Final answer: 58

1. Treat 00111011 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 59.
6. Add those contributions: 0 + 59 = 59.
7. As an unsigned pattern, the same eight bits represent 59.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000101.
11. Answer: signed(00111011) = 59.

Final answer: 59

1. Treat 00111100 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 60.
6. Add those contributions: 0 + 60 = 60.
7. As an unsigned pattern, the same eight bits represent 60.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000100.
11. Answer: signed(00111100) = 60.

Final answer: 60

1. Treat 00111101 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 61.
6. Add those contributions: 0 + 61 = 61.
7. As an unsigned pattern, the same eight bits represent 61.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000011.
11. Answer: signed(00111101) = 61.

Final answer: 61

1. Treat 00111110 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 62.
6. Add those contributions: 0 + 62 = 62.
7. As an unsigned pattern, the same eight bits represent 62.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000010.
11. Answer: signed(00111110) = 62.

Final answer: 62

1. Treat 00111111 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 63.
6. Add those contributions: 0 + 63 = 63.
7. As an unsigned pattern, the same eight bits represent 63.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11000000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11000001.
11. Answer: signed(00111111) = 63.

Final answer: 63