This set tests number systems and binary codes, the base of every digital logic course. It covers conversions between binary, octal, decimal and hexadecimal, signed numbers in 1's and 2's complement, overflow, BCD arithmetic, Gray code and excess-3. The questions suit GATE ECE/CSE aspirants, university semester exams and placement rounds where quick base conversion and complement arithmetic are routinely tested.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 18 questions.
Topics covered in this set
- Binary, octal, decimal and hexadecimal conversion
- 1's and 2's complement representation
- Signed arithmetic and overflow detection
- BCD and BCD addition correction
- Gray code conversion and properties
- Excess-3 and self-complementing codes
- Radix complements and parity bits
Digital Electronics MCQs with answers and explanations
Q1. What is the decimal value of the binary number (10110.101)2?
a) 22.525
b) 21.625
c) 22.75
d) 22.625
Q2. The octal number (725)8 is equal to which hexadecimal number?
a) 1E5
b) 1D5
c) 1D3
d) 2D5
Q3. What is the 8-bit 2's complement representation of -45?
a) 11010010
b) 10101101
c) 11010011
d) 11010100
Q4. What range of integers can be stored in an 8-bit 2's complement register?
a) -127 to +127
b) -128 to +128
c) -128 to +127
d) -127 to +128
Q5. Which of the following signed number representations has two distinct bit patterns for zero?
a) 1's complement
b) 2's complement
c) Excess-127 (biased) code
d) Unsigned binary
Q6. What is the BCD (8421) code for decimal 739?
a) 0111 0011 1010
b) 0111 0011 1001
c) 1011100011
d) 0110 0011 1001
Q7. What is the Gray code equivalent of the binary number 1011?
a) 1101
b) 1001
c) 1110
d) 0110
Q8. The Gray code word 1101 corresponds to which binary number?
a) 1011
b) 1001
c) 1110
d) 1000
Q9. What is the excess-3 code for decimal 58?
a) 0101 1000
b) 1000 1010
c) 0111 1011
d) 1000 1011
Q10. Which of these codes is self-complementing, meaning the 9's complement of a digit is obtained by inverting its bits?
a) Excess-3
b) 8421 BCD
c) Gray code
d) ASCII
Q11. Two BCD digits 0111 and 0110 are added and give 1101. What correction yields the proper BCD result?
a) Add 0110, giving 0001 0011
b) No correction is needed; the result is 1101
c) Add 0011, giving 0001 0000
d) Subtract 0110, giving 0111
Q12. Using 8-bit 2's complement arithmetic, what bit pattern results from computing 25 - 40?
a) 10001111
b) 11110001
c) 11110000
d) 00001111
Q13. Two 8-bit 2's complement numbers 01100100 (+100) and 01000110 (+70) are added. Which statement about the result is correct?
a) No overflow occurs and the result is +170
b) Overflow occurs and the result reads as -84
c) No overflow occurs because there is no carry out of the MSB
d) Overflow occurs and the result reads as -86
Q14. What is the minimum number of bits needed to represent decimal 1000 in unsigned binary?
a) 10
b) 9
c) 11
d) 12
Q15. Why is Gray code preferred for the output of rotary shaft encoders?
a) It is a weighted code that simplifies arithmetic
b) It needs fewer bits than binary for the same range
c) Only one bit changes between consecutive values, avoiding false intermediate readings
d) It is self-complementing
Q16. If (121)b = (49)10, what is the base b?
a) 7
b) 6
c) 8
d) 5
Q17. What is the 10's complement of the 4-digit decimal number 3250?
a) 6749
b) 7750
c) 6750
d) 6760
Q18. A 7-bit data word 1101001 is sent with an even-parity bit placed as the MSB. What 8-bit word is transmitted?
a) 11101001
b) 11010010
c) 11010011
d) 01101001
Quick revision notes
- Binary to octal/hex: group bits in 3s/4s from the binary point outward.
- n-bit 2's complement range: -2^(n-1) to 2^(n-1)-1; 1's complement: -(2^(n-1)-1) to 2^(n-1)-1.
- 2's complement = 1's complement + 1; 1's complement has +0 and -0.
- Overflow in signed addition: carry into MSB differs from carry out of MSB.
- BCD addition: add 0110 when a digit sum exceeds 9 or produces a carry.
- Binary to Gray: g(i) = b(i+1) XOR b(i); Gray to binary: b(i) = b(i+1) XOR g(i).
- Excess-3 = BCD + 0011; it is self-complementing, as is 2421.
- r's complement of N (n digits) = r^n - N; (r-1)'s complement = r^n - 1 - N.
Frequently asked questions
Why do computers use 2's complement instead of sign-magnitude?
2's complement has a single zero and lets the same adder hardware handle both addition and subtraction without separate sign logic. Subtraction becomes adding the 2's complement of the subtrahend.
How do you detect overflow when adding signed binary numbers?
Overflow occurs when two operands of the same sign produce a result of the opposite sign. In hardware it is detected as the XOR of the carry into and the carry out of the sign bit.
What is the difference between BCD and pure binary?
Pure binary converts the whole number to base 2, while BCD encodes each decimal digit separately in 4 bits. BCD wastes six of the sixteen 4-bit combinations but makes decimal display and I/O simpler.
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