Binary and Hexadecimal Representations of Decimal Numbers, Assignments of Digital Systems Design

Instructions for converting decimal numbers to 8-bit binary signed two's complement, hexadecimal, and binary coded decimal (bcd) formats. It also covers the representation of negative numbers using two's complement and the decimal values of the greatest and least numbers representable using 7-bit unsigned and signed two's complement.

Typology: Assignments

Pre 2010

Uploaded on 08/16/2009

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1. Express the following decimal numbers using 8-bit binary signed two’s
complement:
120 36 11.40.325 0.421875
Can all the numbers be represented using only 8 bits? Why or why
not?
2. Convert the following decimal numbers to hexadecimal. The fractional
numbers may not be terminating:
487 321.9 4522081 0.8531
3. Give the value of 011010000101 interpreted as unsigned binary, signed
two’s complement and binary coded decimal (BCD).
4. Obtain the two’s complement of the binary numbers you obtained in
question 1.
5. What is the decimal value of the greatest number representable using
7 bit unsigned binary? Using 7 bit signed two’s complement?
6. What is the decimal value of the least number representable using 7
bit unsigned binary? Using 7 bit signed two’s complement?
7. How is the number (1)10 represented using 4 bit two’s complement?
Using 8 bit two’s complement? Using 64 bit two’s complement?

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  1. Express the following decimal numbers using 8-bit binary signed two’s complement:

Can all the numbers be represented using only 8 bits? Why or why not?

  1. Convert the following decimal numbers to hexadecimal. The fractional numbers may not be terminating:
  1. Give the value of 011010000101 interpreted as unsigned binary, signed two’s complement and binary coded decimal (BCD).
  2. Obtain the two’s complement of the binary numbers you obtained in question 1.
  3. What is the decimal value of the greatest number representable using 7 bit unsigned binary? Using 7 bit signed two’s complement?
  4. What is the decimal value of the least number representable using 7 bit unsigned binary? Using 7 bit signed two’s complement?
  5. How is the number (−1) 10 represented using 4 bit two’s complement? Using 8 bit two’s complement? Using 64 bit two’s complement?