2015S001/User talk:Carterjseay/Homework 2

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Contents

  1. Powers of Two
    1. Find the result of the following and provide the answer in power of two
    2. Find the result of the following and provide the answer in power of two
  2. Converting numbers between different bases
    1. Convert (53)7 to octal (base 8) notation
    2. Convert (BE)16 to binary
  3. The template method
    1. Using the template method, convert 1011012 to its decimal equivalent
    2. Using the template method, convert 14310 to its binary equivalent
    3. Using the extended template method, convert 205.87510 to its binary equivalent
  4. Binary representation of numbers
    1. What is the binary (base 2) number 100111111, written in decimal (base 10)?
    2. What is the largest positive base 10 integer that can be represented with 15 bits?
    3. How many different patterns of 1 and 0 can be produced using 7 bits?
    4. How many bits are needed to represent the base-10 number 1021 ?
    5. How many bit patterns can be formed by 5 bits?
    6. convert (168)10 to its binary equivalent
  5. INTEGER MULTIPLICATION AND DIVISION OF BINARY NUMBERS BY POWERS OF TWO
    1. Multiply 1010112 by 810 and represent the result in binary
    2. Divide 11100102 by 3210 and represent the result in binary
  6. Binary Addition
    1. Add (100101.110101)2 and (11.1101)2 . Express your result in binary
    2. Add (1.625)10 and (0.5625)10 . Express your result in binary
  7. Binary Multiplication
    1. Multiply the binary numbers 0110111 and 1111
    2. Calculate (1010101)2 multiplied by (1024)10 (without using a calculator), and represent the result in integer binary.
  8. Use your creativity to generate 4 problems of your own and provide answers to them, to demonstrate your understanding of binary number conversion and binary number arithmetic.
    1. Q1
    2. Q2
    3. Q3
    4. Q4

1. Powers of Two

1.1. Find the result of the following and provide the answer in power of two

215 x 2-3 x 2-5

all in the power 15-8=7

=2^7

1.2. Find the result of the following and provide the answer in power of two

( 218 x 212 ) / ( 213 x 27 )

18+12=30 13+7=20 30-20=10 =2^10

2. Converting numbers between different bases

2.1. Convert (53)7 to octal (base 8) notation

5x7+3x1=38 base 10

4x8+6x1=38 base 10

46 base 8

2.2. Convert (BE)16 to binary

10*16+14*1=(174) base 10

(10101110) base2

3. The template method

3.1. Using the template method, convert 1011012 to its decimal equivalent

1 0 1 1 0 1
25 24 23 22 21 20
 ?  ?  ?  ?  ?  ?

32+0+8+4+0+1=45

3.2. Using the template method, convert 14310 to its binary equivalent

(143)10 ⇒⇒ (10001111)2

3.3. Using the extended template method, convert 205.87510 to its binary equivalent

(205.875)10 ⇒⇒ (110011010.111)2

Almost. You have an extra 0 before the decimal point that should not be there. The correct ans is 1100 1101.111(-.5 pt)

4. Binary representation of numbers

4.1. What is the binary (base 2) number 100111111, written in decimal (base 10)?

(100111111)base2 ⇒⇒ (319) base10

4.2. What is the largest positive base 10 integer that can be represented with 15 bits?

1,000,000,000,000,000

Good try. However to find the largest positive number, use the formula 2N -1. Where N= the number of bits. So you will get 215 -1. Which is 32767 (base 10) (-1 pt)

4.3. How many different patterns of 1 and 0 can be produced using 7 bits?

128

4.4. How many bits are needed to represent the base-10 number 1021 ?

512+256+128+64+32+16+8+4+0+1

1111111101

10 bits

4.5. How many bit patterns can be formed by 5 bits?

32

4.6. convert (168)10 to its binary equivalent

(10101000) base 2

5. INTEGER MULTIPLICATION AND DIVISION OF BINARY NUMBERS BY POWERS OF TWO

5.1. Multiply 1010112 by 810 and represent the result in binary

101011000

5.2. Divide 11100102 by 3210 and represent the result in binary

11

with Reminder=10010

6. Binary Addition

6.1. Add (100101.110101)2 and (11.1101)2 . Express your result in binary

(101001.101001)2

6.2. Add (1.625)10 and (0.5625)10 . Express your result in binary

(10.0011)2

7. Binary Multiplication

7.1. Multiply the binary numbers 0110111 and 1111

(1100111001)2

7.2. Calculate (1010101)2 multiplied by (1024)10 (without using a calculator), and represent the result in integer binary.

10101010000000000

8. Use your creativity to generate 4 problems of your own and provide answers to them, to demonstrate your understanding of binary number conversion and binary number arithmetic.

8.1. Q1

Convert (AB) base 16 into a base 10

(AB)base16 ⇒⇒ (171)base10

8.2. Q2

Convert (112) base 10 into a binary number.

1110000

8.3. Q3

Multiply 1011011 x 100 = 101101100

8.4. Q4

Add 1011 + 1101 = 11000

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