Q. Using 1's complement get 1010100 - 1000011



Q. Using 1's complement get 1000011 - 1010100




SIGNED BINARY NUMBERS





Points to Remember





Arithmetic Addition





Addition of two signed Binary Numbers







Arithmetic Subtraction




Q: Solve ( - 6 ) - ( -13 )


  1. In binary with eight bits, this operation is written as ( 11111010 - 11110011 )

  2. The subtraction is changed to addition by taking the 2' s complement of the subtrahend (-13), giving ( + 13)

  3. In binary, this is 11111010 + 00001101 = 100000111 Removing the end carry, we obtain the correct answer: 00000111 (+7)



BINARY CODED DECIMAL





Rules of Addition - BCD











Other Decimal Codes






Gray Codes







Additional Notes





Boolean Gates





Solved Question Papers - GATE, UGC-NET, Maharashtra-SET



Q.The representation of the value of a 16-bit unsigned integer X in a hexadecimal number system is (BCA)9. The representation of the value of X in octal number system is:


Answer : D



Q.Given the following binary number in 32 bit (single precision) IEEE-754 format: 00111110011011010000000000000000 The decimal value closest to this floating-point number is:

Answer : C

Solution:

Q.Consider a binary code that consists only four valid codewords as given below. 00000, 01011, 10101, 11110 Let minimum Hamming distance of code be p and maximum number of erroneous bits that can be corrected by the code be q. The value of p and q are:

Answer : A

Solution:



Q. (1217)8 is equivalent to (GATE-CS-2009)

Answer : B



Q. The base (or radix) of the number system such that the following equation holds is____________.
312/20=13.1

Answer : C



Q.Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is _____ .

Answer : C

Q.The addition of 4-bit, two's complement, binary numbers 1101 and 0100 results in (UPSC 2006)

Answer : C

-3 + 4 = 1, so no overflow



Q. A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. If the output bit-string after stuffing is 01111100101, then the input bit-string is

Answer : B



Q. The number of 1's present in the binary representation of 10 * 256 + 5 * 16 + 5 is UGNET JUNE 2011


Answer : C



Q.The decimal number equivalent of (4057.06)8 is

  1. 2095.75
  2. 2095.075
  3. 2095.937
  4. 2095.0937

Answer : D



Q.12-bit 2’s complement of –73.75 is

Answer : C



Q.Encoding of data bits 0011 into 7-bit even Parity Hamming Code is

Answer : A



Q.In octal, the twelve-bit two's complement of the hexadecimal number 2AF is:

Answer : D

Solution: 2AF in hex = 001010101111 . Binary two's complement of 001010101111 = 110101010001. 110101010001 in binary is 6521 in octal.



Q.let an ,an-1 , ........, a1, a0 be the binary representation of an integer 'b' then b is divisible by 3 if:

Answer : D

Solution: by taking examples



Q. In octal,the twelve bit two's complement of the hexdecimal number 2AF16 is : (UPSC 2016 SET B)

  1. 62518
  2. 52618
  3. 65128
  4. 65218

Answer : B



Q. In order that a code is 't' error correcting, the minimum Hamming distance should be : (UGC NET CS 2009)

Answer : D

Solution:

In order that a code is 't' error correcting, the minimum hamming distance should be 2t+1 .



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