Signed eight-bit values

1. Treat 00000000 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 0.
6. Add those contributions: 0 + 0 = 0.
7. As an unsigned pattern, the same eight bits represent 0.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000000.
11. Answer: signed(00000000) = 0.

Final answer: 0

1. Treat 00000001 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 1.
6. Add those contributions: 0 + 1 = 1.
7. As an unsigned pattern, the same eight bits represent 1.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111111.
11. Answer: signed(00000001) = 1.

Final answer: 1

1. Treat 00000010 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 2.
6. Add those contributions: 0 + 2 = 2.
7. As an unsigned pattern, the same eight bits represent 2.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111110.
11. Answer: signed(00000010) = 2.

Final answer: 2

1. Treat 00000011 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 3.
6. Add those contributions: 0 + 3 = 3.
7. As an unsigned pattern, the same eight bits represent 3.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111101.
11. Answer: signed(00000011) = 3.

Final answer: 3

1. Treat 00000100 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 4.
6. Add those contributions: 0 + 4 = 4.
7. As an unsigned pattern, the same eight bits represent 4.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111100.
11. Answer: signed(00000100) = 4.

Final answer: 4

1. Treat 00000101 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 5.
6. Add those contributions: 0 + 5 = 5.
7. As an unsigned pattern, the same eight bits represent 5.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111011.
11. Answer: signed(00000101) = 5.

Final answer: 5

1. Treat 00000110 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 6.
6. Add those contributions: 0 + 6 = 6.
7. As an unsigned pattern, the same eight bits represent 6.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111010.
11. Answer: signed(00000110) = 6.

Final answer: 6

1. Treat 00000111 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 7.
6. Add those contributions: 0 + 7 = 7.
7. As an unsigned pattern, the same eight bits represent 7.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11111000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111001.
11. Answer: signed(00000111) = 7.

Final answer: 7

1. Treat 00001000 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 8.
6. Add those contributions: 0 + 8 = 8.
7. As an unsigned pattern, the same eight bits represent 8.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11111000.
11. Answer: signed(00001000) = 8.

Final answer: 8

1. Treat 00001001 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 9.
6. Add those contributions: 0 + 9 = 9.
7. As an unsigned pattern, the same eight bits represent 9.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110111.
11. Answer: signed(00001001) = 9.

Final answer: 9

1. Treat 00001010 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 10.
6. Add those contributions: 0 + 10 = 10.
7. As an unsigned pattern, the same eight bits represent 10.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110110.
11. Answer: signed(00001010) = 10.

Final answer: 10

1. Treat 00001011 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 11.
6. Add those contributions: 0 + 11 = 11.
7. As an unsigned pattern, the same eight bits represent 11.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110101.
11. Answer: signed(00001011) = 11.

Final answer: 11

1. Treat 00001100 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 12.
6. Add those contributions: 0 + 12 = 12.
7. As an unsigned pattern, the same eight bits represent 12.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110100.
11. Answer: signed(00001100) = 12.

Final answer: 12

1. Treat 00001101 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 13.
6. Add those contributions: 0 + 13 = 13.
7. As an unsigned pattern, the same eight bits represent 13.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110011.
11. Answer: signed(00001101) = 13.

Final answer: 13

1. Treat 00001110 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 14.
6. Add those contributions: 0 + 14 = 14.
7. As an unsigned pattern, the same eight bits represent 14.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110010.
11. Answer: signed(00001110) = 14.

Final answer: 14

1. Treat 00001111 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 15.
6. Add those contributions: 0 + 15 = 15.
7. As an unsigned pattern, the same eight bits represent 15.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11110000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110001.
11. Answer: signed(00001111) = 15.

Final answer: 15

1. Treat 00010000 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 16.
6. Add those contributions: 0 + 16 = 16.
7. As an unsigned pattern, the same eight bits represent 16.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11110000.
11. Answer: signed(00010000) = 16.

Final answer: 16

1. Treat 00010001 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 17.
6. Add those contributions: 0 + 17 = 17.
7. As an unsigned pattern, the same eight bits represent 17.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101111.
11. Answer: signed(00010001) = 17.

Final answer: 17

1. Treat 00010010 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 18.
6. Add those contributions: 0 + 18 = 18.
7. As an unsigned pattern, the same eight bits represent 18.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101110.
11. Answer: signed(00010010) = 18.

Final answer: 18

1. Treat 00010011 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 19.
6. Add those contributions: 0 + 19 = 19.
7. As an unsigned pattern, the same eight bits represent 19.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101101.
11. Answer: signed(00010011) = 19.

Final answer: 19

1. Treat 00010100 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 20.
6. Add those contributions: 0 + 20 = 20.
7. As an unsigned pattern, the same eight bits represent 20.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101100.
11. Answer: signed(00010100) = 20.

Final answer: 20

1. Treat 00010101 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 21.
6. Add those contributions: 0 + 21 = 21.
7. As an unsigned pattern, the same eight bits represent 21.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101011.
11. Answer: signed(00010101) = 21.

Final answer: 21

1. Treat 00010110 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 22.
6. Add those contributions: 0 + 22 = 22.
7. As an unsigned pattern, the same eight bits represent 22.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101010.
11. Answer: signed(00010110) = 22.

Final answer: 22

1. Treat 00010111 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 23.
6. Add those contributions: 0 + 23 = 23.
7. As an unsigned pattern, the same eight bits represent 23.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11101000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101001.
11. Answer: signed(00010111) = 23.

Final answer: 23

1. Treat 00011000 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 24.
6. Add those contributions: 0 + 24 = 24.
7. As an unsigned pattern, the same eight bits represent 24.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11101000.
11. Answer: signed(00011000) = 24.

Final answer: 24

1. Treat 00011001 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 25.
6. Add those contributions: 0 + 25 = 25.
7. As an unsigned pattern, the same eight bits represent 25.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100111.
11. Answer: signed(00011001) = 25.

Final answer: 25

1. Treat 00011010 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 26.
6. Add those contributions: 0 + 26 = 26.
7. As an unsigned pattern, the same eight bits represent 26.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100110.
11. Answer: signed(00011010) = 26.

Final answer: 26

1. Treat 00011011 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 27.
6. Add those contributions: 0 + 27 = 27.
7. As an unsigned pattern, the same eight bits represent 27.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100101.
11. Answer: signed(00011011) = 27.

Final answer: 27

1. Treat 00011100 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 28.
6. Add those contributions: 0 + 28 = 28.
7. As an unsigned pattern, the same eight bits represent 28.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100100.
11. Answer: signed(00011100) = 28.

Final answer: 28

1. Treat 00011101 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 29.
6. Add those contributions: 0 + 29 = 29.
7. As an unsigned pattern, the same eight bits represent 29.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100011.
11. Answer: signed(00011101) = 29.

Final answer: 29

1. Treat 00011110 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 30.
6. Add those contributions: 0 + 30 = 30.
7. As an unsigned pattern, the same eight bits represent 30.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100010.
11. Answer: signed(00011110) = 30.

Final answer: 30

1. Treat 00011111 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 31.
6. Add those contributions: 0 + 31 = 31.
7. As an unsigned pattern, the same eight bits represent 31.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 11100000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 11100001.
11. Answer: signed(00011111) = 31.

Final answer: 31