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Digital Electronics
Number systems

Practice questions from Number systems.

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Q#1 Number systems GATE EC 2024 (Set 1) NAT +1 mark -0 marks

In a number system of base , the equation  has  as one of its solutions. The value of  is_______.

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Q#2 Number systems GATE EC 2021 (Set 1) MCQ +1 mark -0.33 marks

If , where  and  indicate the bases of the corresponding numbers, then        

 and

 and

 and

 and

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Q#3 Number systems GATE EC 2020 (Set 1) MCQ +2 marks -0.66 marks

P, Q, and  are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1's complement, and 2's complement representations, respectively. The 6-bit 2's complement representation of  is

111101

110101

110010

111001

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Q#4 Number systems GATE EC 2014 (Set 2) NAT +1 mark -0 marks

The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is __________ .

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Q#5 Number systems GATE EC 2008 (Set 1) MCQ +2 marks -0.66 marks

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 form is

100000111

00000111

11111001

111111001

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Q#6 Number systems GATE EC 2007 (Set 1) MCQ +1 mark -0.33 marks

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

100111

001000

000111

101001

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Q#7 Number systems GATE EC 2006 (Set 1) MCQ +2 marks -0.66 marks

A new Binary Coded Pentary (BCP) Number systems is proposed in which every digit of a base-5 number is presented 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 100010011001 corresponds to the following number in base-5 system

423

1324

2201

4231

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Q#8 Number systems GATE EC 2005 (Set 1) MCQ +1 mark -0.33 marks

Decimal 43 in Hexadecimal and BCD Number systems is respectively

B2, 0100 0011        

2B, 0100 0011

2B, 0011 0100

B2, 0100 0100

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Q#9 Number systems GATE EC 2004 (Set 1) MCQ +1 mark -0.33 marks

The range of signed decimal numbers that can be represented by 6-bite 1’s complement number is

-31 and +31

-63 and +64

-64 and +63

-32 and +31

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Q#10 Number systems GATE EC 2004 (Set 1) MCQ +1 mark -0.33 marks

A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in 100 increments. The minimum number of bits required to encode, in straight binary is

8

6

5

7

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Q#11 Number systems GATE EC 2004 (Set 1) MCQ +2 marks -0.66 marks

11001, 1001 and 111001 correspond to the 2’s complement representation of which one of the following sets of number?

25, 9 and 57 respectively

-6, -6 and -6 respectively

-7, -7 and -7 respectively

-25, -9 and -57 respectively

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Q#12 Number systems GATE EC 2002 (Set 1) MCQ +1 mark -0.33 marks

4-bit 2’s complement representation of a decimal number is 1000. The number is

+8

0

-7

-8

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Q#13 Number systems GATE EC 2001 (Set 1) MCQ +1 mark -0.33 marks

The 2’s complement representation of -17 is

01110

01111

11110

10001

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Q#14 Number systems GATE EC 1998 (Set 1) MCQ +2 marks -0.66 marks

An equivalent 2’s complement representation of the 2’s complement number 1101 is

110100

001101

110111

111101

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Q#15 Number systems GATE EC 1993 (Set 1) MCQ +2 marks -0.66 marks

2’s complement representation of a 16-bit number (one sign bit and 15 magnitude bits) is FFF7. Its magnitude in decimal representation is

0

1

32,767

65, 535

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