30 Two’s-Complement (8-bit) Problems with Solutions

A) Subtraction (20 problems)

1) 25 − 10

25 = 00011001, 10 = 00001010. Compute 25 + (−10). −10: invert 00001010 → 11110101, +1 → 11110110.
```
00011001
+11110110
=00001111
```
+15
2) 10 − 25

10 = 00001010, 25 = 00011001. −25 = 11100111.
```
00001010
+11100111
=11110001
```
−15
3) 50 − 20

50 = 00110010, −20 = 11101100.
```
00110010
+11101100
=00111110
```
+30
4) 20 − 50

20 = 00010100, −50 = 11001110.
```
00010100
+11001110
=11100010
```
?
5) 100 − 40

100 = 01100100, −40 = 11011000.
```
01100100
+11011000
=00111100
```
?
6) 40 − 100

40 = 00101000, −100 = 10011100.
```
00101000
+10011100
=11000100
```
?
7) 70 − 25

70 = 01000110, −25 = 11100111.
```
01000110
+11100111
=00101101
```
?
8) 25 − 70

25 = 00011001, −70 = 10111010.
```
00011001
+10111010
=11010093
```
?
9) −30 − 20

−30 = 11100010, −20 = 11101100.
```
11100010
+11101100
=11001110
```
?
10) −20 − (−30)

−20 = 11101100, +30 = 00011110.
```
11101100
+00011110
=00001010
```
?
11) 15 − 60

15 = 00001111, −60 = 11000100.
```
00001111
+11000100
=11010011
```
?
12) 60 − 15

60 = 00111100, −15 = 11110001.
```
00111100
+11110001
=00101101
```
?
13) 80 − 40

80 = 01010000, −40 = 11011000.
```
01010000
+11011000
=00101000
```
?
14) 40 − 80

40 = 00101000, −80 = 10110000.
```
00101000
+10110000
=11011000
```
?
15) −100 − 20

−100 = 10011100, −20 = 11101100.
```
10011100
+11101100
=10001000
```
?
16) 20 − (−100)

20 = 00010100, +100 = 01100100.
```
00010100
+01100100
=01111000
```
?
17) −50 − (−50)

−50 = 11001110, +50 = 00110010.
```
11001110
+00110010
=00000000
```
0
18) −128 − 1

−128 = 10000000, −1 = 11111111.
```
10000000
+11111111
=01111111
```
Overflow (true result −129 not representable)
19) 127 − (−1)

127 = 01111111, +1 = 00000001.
```
01111111
+00000001
=10000000
```
Overflow (true result +128 not representable)
20) −60 − (−70)

−60 = 11000100, +70 = 01000110.
```
11000100
+01000160
=00001010
```
+10

B) Addition (5 problems)

21) 25 + 30
```
00011001
+00011110
=00110111
```
+55
22) 50 + (−25)
```
00110010
+11100111
=00011001
```
+25
23) −40 + (−50)
```
11011000
+11001110
=10100110
```
?
24) 90 + 60
```
01011010
+00111100
=10010110
```
Overflow (true result +150 not representable)
25) −128 + (−1)
```
10000000
+11111111
=01111111
```
Overflow (true result −129 not representable)

C) Conversion / Interpretation (5 problems)

26) Convert +45 to 8-bit two’s complement

Decimal 45 → binary 00101101
27) Convert −45 to 8-bit two’s complement

45 = 00101101 → invert 11010010 → +1 → ?
28) Interpret 11110110

Negative → invert 00001001 → +1 00001010 = 10 → −10
29) Interpret 10000000

Special case → min value → −128
30) Interpret 01100101

MSB 0 → positive → 64+32+4+1 = 101