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Digital Circuits Questions and Answers – Arithmetic Operation

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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

Answer: c
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

Answer: d
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

Answer: c
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

Answer: a
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

Answer: a
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

Answer: c
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

Answer: c
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

Answer: d
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

Answer: b
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

Answer: a
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.

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