Signed eight-bit values

1. Treat 01100000 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 96.
6. Add those contributions: 0 + 96 = 96.
7. As an unsigned pattern, the same eight bits represent 96.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10100000.
11. Answer: signed(01100000) = 96.

Final answer: 96

1. Treat 01100001 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 97.
6. Add those contributions: 0 + 97 = 97.
7. As an unsigned pattern, the same eight bits represent 97.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011111.
11. Answer: signed(01100001) = 97.

Final answer: 97

1. Treat 01100010 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 98.
6. Add those contributions: 0 + 98 = 98.
7. As an unsigned pattern, the same eight bits represent 98.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011110.
11. Answer: signed(01100010) = 98.

Final answer: 98

1. Treat 01100011 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 99.
6. Add those contributions: 0 + 99 = 99.
7. As an unsigned pattern, the same eight bits represent 99.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011101.
11. Answer: signed(01100011) = 99.

Final answer: 99

1. Treat 01100100 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 100.
6. Add those contributions: 0 + 100 = 100.
7. As an unsigned pattern, the same eight bits represent 100.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011100.
11. Answer: signed(01100100) = 100.

Final answer: 100

1. Treat 01100101 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 101.
6. Add those contributions: 0 + 101 = 101.
7. As an unsigned pattern, the same eight bits represent 101.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011011.
11. Answer: signed(01100101) = 101.

Final answer: 101

1. Treat 01100110 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 102.
6. Add those contributions: 0 + 102 = 102.
7. As an unsigned pattern, the same eight bits represent 102.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011010.
11. Answer: signed(01100110) = 102.

Final answer: 102

1. Treat 01100111 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 103.
6. Add those contributions: 0 + 103 = 103.
7. As an unsigned pattern, the same eight bits represent 103.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10011000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011001.
11. Answer: signed(01100111) = 103.

Final answer: 103

1. Treat 01101000 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 104.
6. Add those contributions: 0 + 104 = 104.
7. As an unsigned pattern, the same eight bits represent 104.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10011000.
11. Answer: signed(01101000) = 104.

Final answer: 104

1. Treat 01101001 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 105.
6. Add those contributions: 0 + 105 = 105.
7. As an unsigned pattern, the same eight bits represent 105.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010111.
11. Answer: signed(01101001) = 105.

Final answer: 105

1. Treat 01101010 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 106.
6. Add those contributions: 0 + 106 = 106.
7. As an unsigned pattern, the same eight bits represent 106.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010110.
11. Answer: signed(01101010) = 106.

Final answer: 106

1. Treat 01101011 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 107.
6. Add those contributions: 0 + 107 = 107.
7. As an unsigned pattern, the same eight bits represent 107.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010101.
11. Answer: signed(01101011) = 107.

Final answer: 107

1. Treat 01101100 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 108.
6. Add those contributions: 0 + 108 = 108.
7. As an unsigned pattern, the same eight bits represent 108.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010100.
11. Answer: signed(01101100) = 108.

Final answer: 108

1. Treat 01101101 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 109.
6. Add those contributions: 0 + 109 = 109.
7. As an unsigned pattern, the same eight bits represent 109.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010011.
11. Answer: signed(01101101) = 109.

Final answer: 109

1. Treat 01101110 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 110.
6. Add those contributions: 0 + 110 = 110.
7. As an unsigned pattern, the same eight bits represent 110.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010010.
11. Answer: signed(01101110) = 110.

Final answer: 110

1. Treat 01101111 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 111.
6. Add those contributions: 0 + 111 = 111.
7. As an unsigned pattern, the same eight bits represent 111.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10010000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010001.
11. Answer: signed(01101111) = 111.

Final answer: 111

1. Treat 01110000 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 112.
6. Add those contributions: 0 + 112 = 112.
7. As an unsigned pattern, the same eight bits represent 112.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10010000.
11. Answer: signed(01110000) = 112.

Final answer: 112

1. Treat 01110001 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 113.
6. Add those contributions: 0 + 113 = 113.
7. As an unsigned pattern, the same eight bits represent 113.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001111.
11. Answer: signed(01110001) = 113.

Final answer: 113

1. Treat 01110010 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 114.
6. Add those contributions: 0 + 114 = 114.
7. As an unsigned pattern, the same eight bits represent 114.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001110.
11. Answer: signed(01110010) = 114.

Final answer: 114

1. Treat 01110011 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 115.
6. Add those contributions: 0 + 115 = 115.
7. As an unsigned pattern, the same eight bits represent 115.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001101.
11. Answer: signed(01110011) = 115.

Final answer: 115

1. Treat 01110100 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 116.
6. Add those contributions: 0 + 116 = 116.
7. As an unsigned pattern, the same eight bits represent 116.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001100.
11. Answer: signed(01110100) = 116.

Final answer: 116

1. Treat 01110101 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 117.
6. Add those contributions: 0 + 117 = 117.
7. As an unsigned pattern, the same eight bits represent 117.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001011.
11. Answer: signed(01110101) = 117.

Final answer: 117

1. Treat 01110110 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 118.
6. Add those contributions: 0 + 118 = 118.
7. As an unsigned pattern, the same eight bits represent 118.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001010.
11. Answer: signed(01110110) = 118.

Final answer: 118

1. Treat 01110111 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 119.
6. Add those contributions: 0 + 119 = 119.
7. As an unsigned pattern, the same eight bits represent 119.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10001000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001001.
11. Answer: signed(01110111) = 119.

Final answer: 119

1. Treat 01111000 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 120.
6. Add those contributions: 0 + 120 = 120.
7. As an unsigned pattern, the same eight bits represent 120.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000111; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10001000.
11. Answer: signed(01111000) = 120.

Final answer: 120

1. Treat 01111001 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 121.
6. Add those contributions: 0 + 121 = 121.
7. As an unsigned pattern, the same eight bits represent 121.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000110; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000111.
11. Answer: signed(01111001) = 121.

Final answer: 121

1. Treat 01111010 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 122.
6. Add those contributions: 0 + 122 = 122.
7. As an unsigned pattern, the same eight bits represent 122.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000101; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000110.
11. Answer: signed(01111010) = 122.

Final answer: 122

1. Treat 01111011 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 123.
6. Add those contributions: 0 + 123 = 123.
7. As an unsigned pattern, the same eight bits represent 123.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000100; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000101.
11. Answer: signed(01111011) = 123.

Final answer: 123

1. Treat 01111100 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 124.
6. Add those contributions: 0 + 124 = 124.
7. As an unsigned pattern, the same eight bits represent 124.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000011; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000100.
11. Answer: signed(01111100) = 124.

Final answer: 124

1. Treat 01111101 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 125.
6. Add those contributions: 0 + 125 = 125.
7. As an unsigned pattern, the same eight bits represent 125.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000010; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000011.
11. Answer: signed(01111101) = 125.

Final answer: 125

1. Treat 01111110 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 126.
6. Add those contributions: 0 + 126 = 126.
7. As an unsigned pattern, the same eight bits represent 126.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000001; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000010.
11. Answer: signed(01111110) = 126.

Final answer: 126

1. Treat 01111111 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 127.
6. Add those contributions: 0 + 127 = 127.
7. As an unsigned pattern, the same eight bits represent 127.
8. The signed range for eight bits is −128 through +127.
9. Bitwise inversion alone yields 10000000; inversion plus one wraps modulo 256.
10. The eight-bit negated pattern is 10000001.
11. Answer: signed(01111111) = 127.

Final answer: 127