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# Digital Logic - Number representation and computer arithmetic

6:

A decimal number has 25 digits. The number of bits needed for its equivalent binary representation is, approximately

 A. 50 B. 55 C. 85 D. 80 Answer Report Discuss Option: C Explanation : The largest decimal number with 25 digits is 9,999,999,999,999,999,999,999,999. The smallest decimal number in the form 2n-1 which is greater than or equal to that is 19,342,813,113,834,066,795,298,815. That corresponds to 284-1. So, the minimum number of binary bits required to represent the decimal number 25 nines in a row is 84. This is 84 ones in a row. If you want to support negative as well as positive numbers, you will need 85. Click on Discuss to view users comments. ARUMUGAM said: (7:18pm on Wednesday 15th May 2013) Generalised Expalanation:Let k bits are required to represent d digit decimal number.(ie) Let 2 power k = 10 power dApply base 2 logarithm on both sideslog(2 power k) base 2 = log (10 power d) base 2k log2 base 2 = d log 10 base 2As log10 base 2=3.32192 and log2 base2 =1,k=3.32192dHere d=25,k=3.32192*25k=83 Write your comments here:
7:   Decimal number 5 in level parity self correcting code is
 A. 10000 B. 01011 C. 01100 D. 01101 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
8:

The decimal number 80 can be represented in BCD code as

 A. 1000 0001 B. 0101 0000 C. 0010 0001 D. 1000 0000 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
9:

How many fractional digits 2-48 will have?

 A. 24 B. 47 C. 49 D. 48 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
10:

The 10's complement of (715)8 is

 A. 63 B. 539 C. 285 D. 395 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. sandy said: (7:46pm on Friday 3rd May 2013) convert (715)8 to (?)10=7*8^2 1*8^1 5**^0=(461)10now do 9's comp.=999-461=538then do 10's = 1then answer is 539 Write your comments here:

Syllabus covered in this section is-

• Logic functions, Minimization,
• Design and synthesis of combinational and sequential circuits
• Number representation and computer arithmetic (fixed and floating point)
• Propositional (Boolean) Logic
• Satisfiability and Tautology
• Logic Families: TTL, ECL and C-MOS gates.
• Boolean algebra and Minimization of Boolean functions
• Flip-flops-types, race condition and comparison.
• Design of combinational and sequential Circuits
• Representation of Integers: Octal, Hex. Decimal and Binary.
•  2's complement and 1 's complement arithmetic
• Floating point representation.

This Section covers Digital Logic Questions Answers .

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