### Previous GATE Questions on Number Systems & Subtraction using 2's Complement Method (1987 to Till Date)

1987

1.       The subtraction of a binary number Y from another binary number X, done by adding 2’s compliment of Y to X, results in a binary number without overflow. This implies that the result is
a.       Negative and is in normal form
b.      Negative an is in 2’s compliment form
c.       Positive and is in normal form
d.      Positive and is in 2’s compliment form

1993

1.       2’s complement representation of a 16 bit number (one sign bit and 15 magnitude bits) is FFFF. Its magnitude in decimal representation is
a.       0
b.      1
c.       32,767
d.      65,535

1998

1.       An equivalent 2’s complement representation of the 2’s complement number is 1101 is
a.       110100
b.      001101
c.       110111
d.      111101

2.       Two 2’s complement numbers having sign bits x and y are added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function

2001

1.       The 2’s complement representation of – 17  is
a.       01110
b.      101111
c.       11110
d.      10001

2002

1.       4 – bit 2’s complement representation of a decimal number is 1000. The number is
a.       +8
b.      0
c.       -7
d.      -8

2004
1.       The range of signed decimal numbers that can be represented by 6 bit 1’s complement form is
a.       -31 to +31
b.      -63 to +64
c.       -64 to +63
d.      -32 to +31

2.       11001, 1001 and 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
d.      -25, -9 and -57 respectively

2005

1.       Decimal 43 in Hexadecimal and BCD number system is respectively
a.       B2, 0100 0011
b.      2B, 0100 0011
c.       2B, 0011 0100
d.      B2, 0100 0100

2006

1.       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 number system, the BCP code 100010011001 corresponds to the following number in base-5 system
a.       423
b.      1324
c.       2201
d.      4231

2007

1.       X = 01110 and Y = 11001 are two 5 bit binary numbers represented in 2’s compliement format. The sum of X and Y represented in 2’s compliment format using 6 bits is
a.       100111
b.      001000
c.       000111
d.      101001

2008

1.       The two numbers represented in signed 2’s compliment form are P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2’s compliment form is
a.       100000111
b.      00000111
c.       11111001
d.      111111001

2014 (from all 4 sets)

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

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