Digital Electronics/Circuits Multiple Choice Questions 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
Clarification: 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
Clarification: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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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. 0111
Answer: D
Clarification: 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
Clarification:
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
Clarification: 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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