Computer Science: An Overview (13th Edition) (What's New in Computer Science)
Computer Science: An Overview (13th Edition) (What's New in Computer Science)
13th Edition
ISBN: 9780134875460
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
Expert Solution & Answer
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Chapter 1, Problem 33CRP

a.

Explanation of Solution

Convert 5+1 into two’s complement notation, converting any subtraction problem to an equivalent addition problem and perform the addition and convert the answer to base ten notations:

The condition of overflow is:

  • Check the number is positive or negative.
  • When the number is positive, convert the number from base ten to binary.
  • When the number is negative, convert the number from base ten to binary, complement the binary number and add 1.
  • Convert number 1 into two’s complement notation.

2101

  • The binary representation is the sequence of the remainder from down to bottom (1)10=(1)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (1)2=(00001)2
  • The two’s complement notation of 1 is 00001.
  • Convert number 5 into two’s complement notation.

2522121001

  • The binary representation is the sequence of the remainder from down to bottom (5)10</

b.

Explanation of Solution

Convert 51 into two’s complement notation, converting any subtraction problem to an equivalent addition problem and perform the addition and convert the answer to base ten notations:

The condition of overflow is:

  • Check the number is positive or negative.
  • When the number is positive, convert the number from base ten to binary.
  • When the number is negative, convert the number from base ten to binary, complement the binary number and add 1.
  • Convert number 1 into two’s complement notation.

2101

  • The binary representation is the sequence of the remainder from down to bottom (1)10=(1)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (1)2=(00001)2
  • Take the complement of the above binary number.

0000111110

  • Add 1 to the above complement binary number.

11110+111111

  • The two’s complement notation of (1)2 is 11111
  • Convert number 5 into two’s complement notation

c.

Explanation of Solution

Convert 125 into two’s complement notation, converting any subtraction problem to an equivalent addition problem and perform the addition and convert the answer to base ten notations:

The condition of overflow is:

  • Check the number is positive or negative.
  • When the number is positive, convert the number from base ten to binary.
  • When the number is negative, convert the number from base ten to binary, complement the binary number and add 1.
  • Convert number 12 into two’s complement notation.

21226023021101

  • The binary representation is the sequence of the remainder from down to bottom (12)10=(1100)2 .
  • To make the above binary representation to 5 bits, put 0 before the binary number (12)10=(01100)2 .
  • The two’s complement notation of (12)10 is 01100.
  • Convert number 5 into two’s complement notation.

2522121001

  • The binary representation is the sequence of the remainder from down to bottom (5)10=(101)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (5)10=(00101)2
  • Take the complement of the above binary number

d.

Explanation of Solution

Convert 87 into two’s complement notation, converting any subtraction problem to an equivalent addition problem and perform the addition and convert the answer to base ten notations:

The condition of overflow is:

  • Check the number is positive or negative.
  • When the number is positive, convert the number from base ten to binary.
  • When the number is negative, convert the number from base ten to binary, complement the binary number and add 1.
  • Convert number 8 into two’s complement notation.

2824022021001

  • The binary representation is the sequence of the remainder from down to bottom (8)10=(1000)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (8)10=(01000)2
  • The two’s complement notation of (8)10 is 01000.
  • Convert number 7 into two’s complement notation.

2723121101

  • The binary representation is the sequence of the remainder from down to bottom (7)10=(111)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (7)10=(00111)2
  • Take the complement of the above binary number

e.

Explanation of Solution

Convert 12+5 into two’s complement notation, converting any subtraction problem to an equivalent addition problem and perform the addition and convert the answer to base ten notations:

The condition of overflow is:

  • Check the number is positive or negative.
  • When the number is positive, convert the number from base ten to binary.
  • When the number is negative, convert the number from base ten to binary, complement the binary number and add 1.
  • Convert the number 12 into two’s complement notation.

21226023021101

  • The binary representation is the sequence of the remainder from down to bottom (12)10=(1100)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (12)10=(01100)2
  • Take the complement of the above binary number.

0110010011

  • Add 1 to the above complement binary number.

10011+110000

  • The two’s complement notation of (11)10 is 10101

f.

Explanation of Solution

Convert 511 into two’s complement notation, converting any subtraction problem to an equivalent addition problem and perform the addition and convert the answer to base ten notations:

The condition of overflow is:

  • Check the number is positive or negative.
  • When the number is positive, convert the number from base ten to binary.
  • When the number is negative, convert the number from base ten to binary, complement the binary number and add 1.
  • Convert the number 11  into two’s complement notation.

21125122121001

  • The binary representation is the sequence of the remainder from down to bottom (11)10=(1011)2
  • To make the above binary representation to 5 bits, put 0 before the binary number (11)10=(01011)2
  • Take the complement of the above binary number.

0101110100

  • Add 1 to the above complement binary number.

10100+110101

  • The two’s complement notation of (11)10 is 10101

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Chapter 1 Solutions

Computer Science: An Overview (13th Edition) (What's New in Computer Science)

Ch. 1.3 - Prob. 1QECh. 1.3 - Prob. 2QECh. 1.3 - Prob. 3QECh. 1.3 - Prob. 4QECh. 1.3 - Prob. 5QECh. 1.3 - Prob. 6QECh. 1.4 - Here is a message encoded in ASCII using 8 bits...Ch. 1.4 - In the ASCII code, what is the relationship...Ch. 1.4 - Prob. 3QECh. 1.4 - Prob. 4QECh. 1.4 - Convert each of the following binary...Ch. 1.4 - Prob. 6QECh. 1.4 - What is the largest numeric value that could be...Ch. 1.4 - An alternative to hexadecimal notation for...Ch. 1.4 - What is an advantage of representing images via...Ch. 1.4 - Prob. 10QECh. 1.5 - Convert each of the following binary...Ch. 1.5 - Convert each of the following base ten...Ch. 1.5 - Convert each of the following binary...Ch. 1.5 - Express the following values in binary notation:...Ch. 1.5 - Perform the following additions in binary...Ch. 1.6 - Convert each of the following twos complement...Ch. 1.6 - Prob. 2QECh. 1.6 - Suppose the following bit patterns represent...Ch. 1.6 - Suppose a machine stores numbers in twos...Ch. 1.6 - In the following problems, each bit pattern...Ch. 1.6 - Prob. 6QECh. 1.6 - Prob. 7QECh. 1.6 - Prob. 8QECh. 1.6 - Prob. 9QECh. 1.6 - Prob. 10QECh. 1.6 - Prob. 11QECh. 1.7 - Prob. 1QECh. 1.7 - Prob. 3QECh. 1.7 - Prob. 4QECh. 1.8 - What makes Python an interpreted programming...Ch. 1.8 - Write Python statements that print the following:...Ch. 1.8 - Write Python statements to make the following...Ch. 1.8 - Write a Python statement that given an existing...Ch. 1.9 - Prob. 1QECh. 1.9 - Prob. 2QECh. 1.9 - Prob. 3QECh. 1.9 - Prob. 4QECh. 1.9 - Prob. 5QECh. 1.9 - Prob. 6QECh. 1.9 - Prob. 7QECh. 1.10 - Prob. 1QECh. 1.10 - Could errors have occurred in a byte from Question...Ch. 1.10 - Prob. 3QECh. 1.10 - Prob. 4QECh. 1.10 - Prob. 5QECh. 1.10 - Prob. 6QECh. 1 - Determine the output of each of the following...Ch. 1 - a. What Boolean operation does the circuit...Ch. 1 - a. If we were to purchase a flip-flop circuit from...Ch. 1 - Assume that both of the inputs in the following...Ch. 1 - The following table represents the addresses and...Ch. 1 - How many cells can be in a computers main memory...Ch. 1 - Prob. 7CRPCh. 1 - Prob. 8CRPCh. 1 - Prob. 9CRPCh. 1 - Prob. 10CRPCh. 1 - Suppose a picture is represented on a display...Ch. 1 - Prob. 12CRPCh. 1 - Prob. 13CRPCh. 1 - If each sector on a magnetic disk contains 1024...Ch. 1 - How many bytes of storage space would be required...Ch. 1 - Prob. 16CRPCh. 1 - Prob. 17CRPCh. 1 - Suppose a typist could type 60 words per minute...Ch. 1 - Prob. 19CRPCh. 1 - Prob. 20CRPCh. 1 - Prob. 21CRPCh. 1 - Prob. 22CRPCh. 1 - Prob. 23CRPCh. 1 - Prob. 24CRPCh. 1 - Prob. 25CRPCh. 1 - Prob. 26CRPCh. 1 - Prob. 27CRPCh. 1 - Prob. 28CRPCh. 1 - Prob. 29CRPCh. 1 - Prob. 30CRPCh. 1 - Prob. 31CRPCh. 1 - Prob. 32CRPCh. 1 - Prob. 33CRPCh. 1 - Prob. 34CRPCh. 1 - Prob. 35CRPCh. 1 - Prob. 36CRPCh. 1 - Prob. 37CRPCh. 1 - Prob. 38CRPCh. 1 - Prob. 39CRPCh. 1 - Prob. 40CRPCh. 1 - Prob. 41CRPCh. 1 - Prob. 42CRPCh. 1 - Prob. 43CRPCh. 1 - Prob. 44CRPCh. 1 - Prob. 45CRPCh. 1 - What would be the hexadecimal representation of...Ch. 1 - Prob. 47CRPCh. 1 - Prob. 48CRPCh. 1 - Prob. 49CRPCh. 1 - Prob. 50CRPCh. 1 - Prob. 51CRPCh. 1 - Prob. 52CRPCh. 1 - Prob. 53CRPCh. 1 - Prob. 54CRPCh. 1 - Prob. 55CRPCh. 1 - Prob. 56CRPCh. 1 - Prob. 57CRPCh. 1 - Prob. 58CRPCh. 1 - Write and test a Python script that, given a...Ch. 1 - Prob. 61CRPCh. 1 - Prob. 2SICh. 1 - Prob. 3SICh. 1 - Prob. 4SICh. 1 - Prob. 5SICh. 1 - Prob. 6SICh. 1 - Prob. 7SI
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