Signed eight-bit values

1. Treat 11100000 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 96.
6. Add those contributions: -128 + 96 = -32.
7. As an unsigned pattern, the same eight bits represent 224.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00100000.
11. Answer: signed(11100000) = -32.

Final answer: -32

1. Treat 11100001 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 97.
6. Add those contributions: -128 + 97 = -31.
7. As an unsigned pattern, the same eight bits represent 225.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011111.
11. Answer: signed(11100001) = -31.

Final answer: -31

1. Treat 11100010 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 98.
6. Add those contributions: -128 + 98 = -30.
7. As an unsigned pattern, the same eight bits represent 226.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011110.
11. Answer: signed(11100010) = -30.

Final answer: -30

1. Treat 11100011 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 99.
6. Add those contributions: -128 + 99 = -29.
7. As an unsigned pattern, the same eight bits represent 227.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011101.
11. Answer: signed(11100011) = -29.

Final answer: -29

1. Treat 11100100 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 100.
6. Add those contributions: -128 + 100 = -28.
7. As an unsigned pattern, the same eight bits represent 228.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011100.
11. Answer: signed(11100100) = -28.

Final answer: -28

1. Treat 11100101 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 101.
6. Add those contributions: -128 + 101 = -27.
7. As an unsigned pattern, the same eight bits represent 229.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011011.
11. Answer: signed(11100101) = -27.

Final answer: -27

1. Treat 11100110 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 102.
6. Add those contributions: -128 + 102 = -26.
7. As an unsigned pattern, the same eight bits represent 230.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011010.
11. Answer: signed(11100110) = -26.

Final answer: -26

1. Treat 11100111 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 103.
6. Add those contributions: -128 + 103 = -25.
7. As an unsigned pattern, the same eight bits represent 231.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00011000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011001.
11. Answer: signed(11100111) = -25.

Final answer: -25

1. Treat 11101000 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 104.
6. Add those contributions: -128 + 104 = -24.
7. As an unsigned pattern, the same eight bits represent 232.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00011000.
11. Answer: signed(11101000) = -24.

Final answer: -24

1. Treat 11101001 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 105.
6. Add those contributions: -128 + 105 = -23.
7. As an unsigned pattern, the same eight bits represent 233.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010111.
11. Answer: signed(11101001) = -23.

Final answer: -23

1. Treat 11101010 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 106.
6. Add those contributions: -128 + 106 = -22.
7. As an unsigned pattern, the same eight bits represent 234.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010110.
11. Answer: signed(11101010) = -22.

Final answer: -22

1. Treat 11101011 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 107.
6. Add those contributions: -128 + 107 = -21.
7. As an unsigned pattern, the same eight bits represent 235.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010101.
11. Answer: signed(11101011) = -21.

Final answer: -21

1. Treat 11101100 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 108.
6. Add those contributions: -128 + 108 = -20.
7. As an unsigned pattern, the same eight bits represent 236.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010100.
11. Answer: signed(11101100) = -20.

Final answer: -20

1. Treat 11101101 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 109.
6. Add those contributions: -128 + 109 = -19.
7. As an unsigned pattern, the same eight bits represent 237.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010011.
11. Answer: signed(11101101) = -19.

Final answer: -19

1. Treat 11101110 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 110.
6. Add those contributions: -128 + 110 = -18.
7. As an unsigned pattern, the same eight bits represent 238.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010010.
11. Answer: signed(11101110) = -18.

Final answer: -18

1. Treat 11101111 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 111.
6. Add those contributions: -128 + 111 = -17.
7. As an unsigned pattern, the same eight bits represent 239.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00010000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010001.
11. Answer: signed(11101111) = -17.

Final answer: -17

1. Treat 11110000 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 112.
6. Add those contributions: -128 + 112 = -16.
7. As an unsigned pattern, the same eight bits represent 240.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00010000.
11. Answer: signed(11110000) = -16.

Final answer: -16

1. Treat 11110001 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 113.
6. Add those contributions: -128 + 113 = -15.
7. As an unsigned pattern, the same eight bits represent 241.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001111.
11. Answer: signed(11110001) = -15.

Final answer: -15

1. Treat 11110010 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 114.
6. Add those contributions: -128 + 114 = -14.
7. As an unsigned pattern, the same eight bits represent 242.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001110.
11. Answer: signed(11110010) = -14.

Final answer: -14

1. Treat 11110011 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 115.
6. Add those contributions: -128 + 115 = -13.
7. As an unsigned pattern, the same eight bits represent 243.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001101.
11. Answer: signed(11110011) = -13.

Final answer: -13

1. Treat 11110100 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 116.
6. Add those contributions: -128 + 116 = -12.
7. As an unsigned pattern, the same eight bits represent 244.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001100.
11. Answer: signed(11110100) = -12.

Final answer: -12

1. Treat 11110101 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 117.
6. Add those contributions: -128 + 117 = -11.
7. As an unsigned pattern, the same eight bits represent 245.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001011.
11. Answer: signed(11110101) = -11.

Final answer: -11

1. Treat 11110110 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 118.
6. Add those contributions: -128 + 118 = -10.
7. As an unsigned pattern, the same eight bits represent 246.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001010.
11. Answer: signed(11110110) = -10.

Final answer: -10

1. Treat 11110111 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 119.
6. Add those contributions: -128 + 119 = -9.
7. As an unsigned pattern, the same eight bits represent 247.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00001000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001001.
11. Answer: signed(11110111) = -9.

Final answer: -9

1. Treat 11111000 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 120.
6. Add those contributions: -128 + 120 = -8.
7. As an unsigned pattern, the same eight bits represent 248.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00001000.
11. Answer: signed(11111000) = -8.

Final answer: -8

1. Treat 11111001 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 121.
6. Add those contributions: -128 + 121 = -7.
7. As an unsigned pattern, the same eight bits represent 249.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000111.
11. Answer: signed(11111001) = -7.

Final answer: -7

1. Treat 11111010 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 122.
6. Add those contributions: -128 + 122 = -6.
7. As an unsigned pattern, the same eight bits represent 250.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000110.
11. Answer: signed(11111010) = -6.

Final answer: -6

1. Treat 11111011 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 123.
6. Add those contributions: -128 + 123 = -5.
7. As an unsigned pattern, the same eight bits represent 251.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000101.
11. Answer: signed(11111011) = -5.

Final answer: -5

1. Treat 11111100 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 124.
6. Add those contributions: -128 + 124 = -4.
7. As an unsigned pattern, the same eight bits represent 252.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000100.
11. Answer: signed(11111100) = -4.

Final answer: -4

1. Treat 11111101 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 125.
6. Add those contributions: -128 + 125 = -3.
7. As an unsigned pattern, the same eight bits represent 253.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000011.
11. Answer: signed(11111101) = -3.

Final answer: -3

1. Treat 11111110 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 126.
6. Add those contributions: -128 + 126 = -2.
7. As an unsigned pattern, the same eight bits represent 254.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000010.
11. Answer: signed(11111110) = -2.

Final answer: -2

1. Treat 11111111 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 127.
6. Add those contributions: -128 + 127 = -1.
7. As an unsigned pattern, the same eight bits represent 255.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 00000000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 00000001.
11. Answer: signed(11111111) = -1.

Final answer: -1