# Digital Circuits Questions and Answers – 1’s, 2’s, 9’s & 10’s Complements – 1

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “1’s, 2’s, 9’s & 10’s Complements – 1”.

1. 1’s complement of 1011101 is ____________
a) 0101110
b) 1001101
c) 0100010
d) 1100101

Explanation: 1’s complement of a binary number is obtained by reversing the binary bits. All the 1’s to 0’s and 0’s to 1’s.Thus, 1’s complement of 1011101 = 0100010.

2. 2’s complement of 11001011 is ____________
a) 01010111
b) 11010100
c) 00110101
d) 11100010

Explanation: 2’s complement of a binary number is obtained by finding the 1’s complement of the number and then adding 1 to it.
2’s complement of 11001011 = 00110100 + 1 = 00110101.

3. On subtracting (01010)2 from (11110)2 using 1’s complement, we get ____________
a) 01001
b) 11010
c) 10101
d) 10100

Explanation: Steps For Subtraction using 1’s complement are:
-> 1’s complement of the subtrahend is determined and added to the minuend.
-> If the result has a carry, then it is dropped and 1 is added to the last bit of the result.
-> Else, if there is no carry, then 1’s complement of the result is found out and a ‘-’ sign preceeds the result.

```                                             1 1 1
Minuend -              1 1 1 1 0
1’s complement of subtrahend -              1 0 1 0 1
____________
Carry over -     1         1 0 0 1 1
1
_____________
1 0 1 0 0```

4. On subtracting (010110)2 from (1011001)2 using 2’s complement, we get ____________
a) 0111001
b) 1100101
c) 0110110
d) 1000011

Explanation: Steps For Subtraction using 2’s complement are:
-> 2’s complement of the subtrahend is determined and added to the minuend.
-> If the result has a carry, then it is dropped and the result is positive.
-> Else, if there is no carry, then 2’s complement of the result is found out and a ‘-’ sign preceeds the result.

```      1’s complement of subtrahend -              1 1 0 1 0 0 1
_________________
1 1 1
Minuend -              1 0 1 1 0 0 1
2’s complement of subtrahend -              1 1 0 1 0 1 0
_________________

Carry over -    1         1 0 0 0 0 1 1

5. On subtracting (001100)2 from (101001)2 using 2’s complement, we get ____________
a) 1101100
b) 011101
c) 11010101
d) 11010111

Explanation: Steps For Subtraction using 2’s complement are:
-> 2’s complement of the subtrahend is determined and added to the minuend.
-> If the result has a carry, then it is dropped and the result is positive.
-> Else, if there is no carry, then 2’s complement of the result is found out and a ‘-’ sign preceeds the result.

```      1’s complement of subtrahend -              1 1 0 0 1 1
_________________
Minuend -              1 0 1 0 0 1
2’s complement of subtrahend -              1 1 0 1 0 0
_________________
Carry over -    1         0 1 1 1 0 1

6. On addition of 28 and 18 using 2’s complement, we get ____________
a) 00101110
b) 0101110
c) 00101111
d) 1001111

Explanation: Steps for Binary Addition Using 2’s complement:
-> The binary equivalent of the two numbers are obtained and added using the rules of binary addition.

```Augend -        0   0 1 1 1 0 0

Addend -        0   0 1 0 0 1 0
_________________
0   1 0 1 1 1 0

Answer: 0  1 0 1 1 1 0```

7. On addition of +38 and -20 using 2’s complement, we get ____________
a) 11110001
b) 100001110
c) 010010
d) 110101011

Explanation: Steps for Binary Addition Using 2’s complement:
-> The 2’s complement of the addend is found out and added to the first number.
-> The result is the 2’s complement of the sum obtained.

```                     Augend -           0 1 0 0 1 1 0
2’s Complement of Subtrahend:           1 1 0 1 1 0 0
_________________
1         0 0 1 0 0 1 0

Answer: 0 1 0 0 1 0```

8. On addition of -46 and +28 using 2’s complement, we get ____________
a) -10010
b) -00101
c) 01011
d) 0100101

Explanation: The BCD form is written of the two given numbers, in their signed form. After which, normal binary addition is performed.
Augend is 28 and Subtrahend is -46.

```                            Augend -           0 0 1 1 1 0 0   .....(a)
2’s Complement of Subtrahend:            1 0 1 0 0 1 0   .....(b)
_________________
Addiing (a) and (b):            1 1 0 1 1 1 0
Since, there is no carry, so answer will be negative
and 2's complement of the above result is determined.
0 0 1 0 0 0 1
+               1
_________________
0 0 1 0 0 1 0

Answer: - 1 0 0 1 0```

9. On addition of -33 and -40 using 2’s complement, we get ____________
a) 1001110
b) -110101
c) 0110001
d) -1001001

Explanation: The BCD form is written of the two given numbers, in their signed form. After which, normal binary addition is performed.
Augend is -40 and Subtrahend is -33.

```                            Augend -           1    0 1 0 0 0 0 1   .....(a)
2’s Complement of Subtrahend:            1    1 0 1 1 0 0 1   .....(b)
______________________
Addiing (a) and (b):           1 0   1 0 0 1 0 0 0
Since, there is no carry, so answer will be negative
and 2's complement of the above result is determined.
1 0 0 1 0 0 0
+               1
_________________
1 0 0 1 0 0 1

10. On subtracting +28 from +29 using 2’s complement, we get ____________
a) 11111010
b) 111111001
c) 100001
d) 1

Explanation: Steps For Subtraction using 2’s complement are:
-> 2’s complement of the subtrahend is determined and added to the minuend.
-> If the result has a carry, then it is dropped and the result is positive.
-> Else, if there is no carry, then 2’s complement of the result is found out and a ‘-’ sign preceeds the result.

```         1’s complement of subtrahend -        1 0 0 0 1 1
Minuend -        0 1 1 1 0 1
2’s complement of subtrahend -        1 0 0 1 0 0
____________________

Carry over -    1   0 0 0 0 0 1