# Digital Circuits Questions and Answers – Arithmetic Operation

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Arithmetic Operation”

1. What is the addition of the binary numbers 11011011010 and 010100101?
a) 0111001000
b) 1100110110
c) 11101111111
d) 10011010011

Explanation: The rules for Binary Addition are :
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 ( Carry 1)

```       1
1 1 0 1 1 0 1 1 0 1 0
+ 0 0 0 1 0 1 0 0 1 0 1
_______________________
1 1 1 0 1 1 1 1 1 1 1
_______________________```

2. Perform binary addition: 101101 + 011011 = ?
a) 011010
b) 1010100
c) 101110
d) 1001000

Explanation:The rules for Binary Addition are :
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 ( Carry 1)

``` 1 1 1 1 1 1
1 0 1 1 0 1
+ 0 1 1 0 1 1
_______________
1 0 0 1 0 0 0
_______________```

Therefore, the addition of 101101 + 011011 = 1001000.

3. Perform binary subtraction: 101111 – 010101 = ?
a) 100100
b) 010101
c) 011010
d) 011001

Explanation: The rules for Binary Subtraction are :
0 – 0 = 0
0 – 1 = 1 ( Borrow 1)
1 – 0 = 1
1 – 1 = 0

```  1 0 1 1 1 1
- 0 1 0 1 0 1
____________
0 1 1 0 1 0
_____________```

Therefore, The subtraction of 101111 – 010101 = 011010.

4. Binary subtraction of 100101 – 011110 is
a) 000111
b) 111000
c) 010101
d) 101010

Explanation: The rules for Binary Subtraction are :
0 – 0 = 0
0 – 1 = 1 ( Borrow 1)
1 – 0 = 1
1 – 1 = 0

```  1 0 0 1 0 1
- 0 1 1 1 1 0
___________
0 0 0 1 1 1
___________```

Therefore, The subtraction of 100101 – 011110 = 000111.

5. Perform multiplication of the binary numbers: 01001 × 01011 = ?
a) 001100011
b) 110011100
c) 010100110
d) 101010111

Explanation: The rules for binary multiplication are:
0 * 0 = 0
0 * 1 = 0
1 * 0 = 0
1 * 1 = 1

```               0 1 0 0 1
x 0 1 0 1 1
____________
0 1 0 0 1
0 1 0 0 1 0
0 0 0 0 0 0 0
0 1 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0
___________________
0 0 1 1 0 0 0 1 1
___________________```

Therefore, 01001 × 01011 = 001100011.

6. 100101 × 0110 = ?
a) 1011001111
b) 0100110011
c) 101111110
d) 0110100101

Explanation: The rules for binary multiplication are:
0 * 0 = 0
0 * 1 = 0
1 * 0 = 0
1 * 1 = 1

```                      1 0 0 1 0 1
x        0 1 1 0
___________
0 0 0 0 0 0
1 0 0 1 0 1 0
1 0 0 1 0 1 0 0
0 0 0 0 0 0 0 0 0
__________________
0 1 1 0 1 1 1 1 0
___________________```

Therefore, 100101 x 0110 = 011011110.

7. On multiplication of (10.10) and (01.01), we get
a) 101.0010
b) 0010.101
c) 011.0010
d) 110.0011

Explanation: The rules for binary multiplication are:
0 * 0 = 0
0 * 1 = 0
1 * 0 = 0
1 * 1 = 1

```           1 0.1 0
x    0 1.0 1
__________
1 0 1 0
0 0 0 0 0
1 0 1 0 0 0
0 0 0 0 0 0 0
_______________
0 1 1.0 0 1 0
_________________```

Therefore, 10.10 x 01.01 = 011.0010.

8. Divide the binary numbers: 111101 ÷ 1001 and find the remainder
a) 0010
b) 1010
c) 1100
d) 0011

Explanation: Binary Division is accomplished using long division method.

```1 0 0 1 ) 1 1 1 1 0 1 ( 1 1
1 0 0 1
__________
0 1 1 0 0
1 0 0 1
___________
0 1 1 1```

Therefore, the remainder of 111101 ÷ 1001 = 0111.

9. Divide the binary number (011010000) by (0101) and find the quotient
a) 100011
b) 101001
c) 110010
d) 010001

Explanation:

```0 1 0 1 ) 0 1 1 0 1 0 0 0 0 ( 0 1 0 1 1 1
0 0 0 0
_____________________
0 1 1 0 1
0 0 1 0 1
______________
0 1 0 0 0 0
0 0 0 0 0 0
______________________
1 0 0 0 0
0 0 1 0 1
____________________
0 1 0 1 1 0
0 0 0 1 0 1
____________________
1 0 0 0 1 0
0 0 0 1 0 1
________________________
1 1 1 0 1 0
0 0 0 1 0 1
________________________
1 0 1 0 1
0 0 1 0 1
________________________
1 0 0 0 0```

Therefore, the quotient of 011010000 ÷ 1001 = 101001.

10. Binary subtraction of 101101 – 001011 = ?
a) 100010
b) 010110
c) 110101
d) 101100

Explanation: The rules for binary subtraction are:
0 – 0 = 0
0 – 1 = 1 ( Borrow 1)
1 – 0 = 1
1 – 1 = 0

```  1 0 1 1 0 1
- 0 0 1 0 1 1
____________
1 0 0 0 1 0
____________```

Therefore, the subtraction of 101101 – 001011 = 100010.

Scroll to Top