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GATE CLASSES ASSIGNMENT – Digital electronics(Number system)-1
Q 1-15 carries 1 mark each, Q 16-20 carries 2 marks each
Q1. BCD code for decimal number 874 is
(A)100001110100
(B)100011110100
(C)100011100100
(D)011101110010
Q2. 4 - bit 2’s complement representation of a decimal number is 1000. The number is
(A) +8
(B) 0
(C) -7
(C) -7
(D) -8 (GATE-EC-2002)
Q3. Gray code for binary number 101011 is
(A)101011
Q3. Gray code for binary number 101011 is
(A)101011
(B)110101
(C)011111
(C)011111
(D)111110
Q4. Gray code of (A5)16 is equivalent to
(A) 10010101
Q4. Gray code of (A5)16 is equivalent to
(A) 10010101
(B)11010101
(C)11011111
(C)11011111
(D)11011011
Q5. The Octal equivalent of hexadecimal number AB.CD is
(A) 253.314
Q5. The Octal equivalent of hexadecimal number AB.CD is
(A) 253.314
(B) 253.632
(C) 526.314
(C) 526.314
(D) 526.632
Q6. The two numbers represented in signed 2’s complement form are P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2’s complement is.
(A) 1000001111
Q6. The two numbers represented in signed 2’s complement form are P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2’s complement is.
(A) 1000001111
(B) 00000111
(C) 11111001
(C) 11111001
(D) 111111001 (GATE – EC - 2015)
Q7. .X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits is
(A) 100111
Q7. .X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits is
(A) 100111
(B) 001000
(C) 000111
(C) 000111
(D) 101001 (GATE – EC - 2007)
Q8. Which of the following number is not allowed in radix – 7 (base 7) system.
(A)739
Q8. Which of the following number is not allowed in radix – 7 (base 7) system.
(A)739
(B) 463
(C)142
(C)142
(D)666
Q9. A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base- 5 number is represented by its corresponding 3-bit binary code. For example, the base-5 number 24 will be represented by its BCP code 010100. In this numbering system, the BCP code 10001001101 corresponds of the following number is base-5 system
(A) 423
Q9. A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base- 5 number is represented by its corresponding 3-bit binary code. For example, the base-5 number 24 will be represented by its BCP code 010100. In this numbering system, the BCP code 10001001101 corresponds of the following number is base-5 system
(A) 423
(B) 1324
(C) 2201
(C) 2201
(D) 4231 (GATE-EC-2006)
Q10. Decimal equivalent of a 6 bit binary no 100101 if it is in signed magnitude representation is
(A)37
Q10. Decimal equivalent of a 6 bit binary no 100101 if it is in signed magnitude representation is
(A)37
(B)26
(C)-5
(C)-5
(D)27
Q11. Decimal 43 in Hexadecimal and BCD number system is respectively
(A) B2, 0100 011
Q11. Decimal 43 in Hexadecimal and BCD number system is respectively
(A) B2, 0100 011
(B) 2B, 0100 0011
(C) 2B, 0011 0100
(D) B2, 0100 0100 (GATE-EC-2005)
Q12. The range of signed decimal numbers that can be represented by 6-bits 1’s complement number is
(A) -31 to +31
Q12. The range of signed decimal numbers that can be represented by 6-bits 1’s complement number is
(A) -31 to +31
(B) -63 to +63
(C) -64 to +63
(C) -64 to +63
(D) -32 to +31 (GATE-EC-2004)
Q13. 11001, 1001, 111001 correspond to the 2’s complement representation of which one of the following sets of number
(A) 25,9, and 57 respectively
Q13. 11001, 1001, 111001 correspond to the 2’s complement representation of which one of the following sets of number
(A) 25,9, and 57 respectively
(B) -6, -6, and -6 respectively
(C) -7, -7 and -7 respectively
(C) -7, -7 and -7 respectively
(D) -25, -9 and -57 respectively
Q14. 2’s Complement representation of -17 is
(A)100001
Q14. 2’s Complement representation of -17 is
(A)100001
(B)101111
(C)110011
(C)110011
(D)101110 (GATE EC-2001)
Q15. Subtraction of two hexadecimal numbers 8416 – 2A 16result in
Q15. Subtraction of two hexadecimal numbers 8416 – 2A 16result in
(A)2B16
(B)3A16
(C)4B16
(C)4B16
(D)5A16
Q16. Convert decimal 41.6875 in octal
(A)51.54
Q16. Convert decimal 41.6875 in octal
(A)51.54
(B)51.13
(C)54.13
(C)54.13
(D)52.51
Q17. 73x (in base x system) is equal to 54y (in base y system), possible value of x and y
(A)8 and 16
Q17. 73x (in base x system) is equal to 54y (in base y system), possible value of x and y
(A)8 and 16
(B)10 and 12
(C)9 and 13
(C)9 and 13
D)8 and 11
Q18. What is the addition of (-64)10 and (80)16
(A)(-16)10
Q18. What is the addition of (-64)10 and (80)16
(A)(-16)10
(B)(16) 16
(C)(1100000)2
(D)(0100000)2
Q19 In signed magnitude representation, the binary equivalent of 22.5625 is (the bit before comma represents the sign)
(A) 0, 10110.1011
Q19 In signed magnitude representation, the binary equivalent of 22.5625 is (the bit before comma represents the sign)
(A) 0, 10110.1011
(B) 0, 10110.1001
(C) 1, 10101.1001
(C) 1, 10101.1001
(D) 1, 10110.1001 (IES –EC- 2002)
Q20. If (2.3)4 + (1.2) 4 = y4, then value of y in base 4 system,
Q20. If (2.3)4 + (1.2) 4 = y4, then value of y in base 4 system,
(A)10.1
(B)10.01
(C)10.2
(C)10.2
(D)1.02
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