text: # Binary to Decimal Conversion Based on New Paper 1 Syllabus for 2021
  
  Dr. Manishika Jain- Join online Paper 1 intensive course. Includes tests and expected questions.
  
  ## 1՚S & 2՚S Complement
  
  ### Convert to Binary: 2432 (Unsigned)
  
  Ans: 100110000000
  
  2048,256, 128
  
  Check if number is even its lsb would be 0 else would be 1
  
  ### Convert to Decimal: 11011001 (Unsigned)
  
  Ans: 11011001 = 217
  
  2048,256, 128
  
  Check if number is even its lsb would be 0 else would be 1
  
  ### The Negatives! !
  
  1. Signed Magnitude (5 bit machine)
  2. 1՚s Complement (5 bit machine)
  3. 2՚s Complement (5 bit machine)
  
  -5 Singed magnitude- 10101,1՚s Complement: 11010,2՚s complement: 11011.
  
  10101 signed magnitude:-5,1՚s Complement:-10,2՚s Complement -11
  
  2՚s Complement = 1՚s Complement + 1
  
  Negative numbers always have 1 in MSB!
  
  In all numbers + ve remain the same as unsigned
  
  ### The Negatives: Signed Magnitude
  
  -5 Singed magnitude: 10101
  
  -15 Singed magnitude: 11111
  
  11011:-11
  
  ### 01011: 11 the Negatives: 1՚S Complement
  
  -5 1՚s Complement: 11010 (Need machine
  
  width- guess from choices)
  
  -15 1՚s Complement: 10000 (More width would produce more 1՚s)
  
  11011:-4 (MSB is one so negative number, complement and find answer) If no 1 in MSB then simply write 11
  
  01011: 11 (Same as unsigned)
  
  ## The Negatives: 2՚S Complement
  
  -5 2՚s Complement: 11011 (Need machine width- guess from choices) (Add one to 1՚s Complement only for negative numbers)
  
  -15 2՚s Complement: 10001 (More width would produce more 1՚s)
  
  11011:-5 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 11
  
  11110:-2 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 14
  
  01011: 11 (Same as unsigned)
  
  ### Next Class
  
  -5 2՚s Complement: 11011 (Need machine width- guess from choices) (Add one to 1՚s Complement only for negative numbers)
  
  -15 2՚s Complement: 10001 (More width would produce more 1՚s)
  
  11011:-5 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 11
  
  11110:-2 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 14
  
  01011: 11 (Same as unsigned)
  
  Developed by:
explanation: The document contains a series of binary to decimal conversion examples and explanations, including signed and unsigned numbers, 1's complement, and 2's complement. It includes both questions and their corresponding answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Binary to Decimal Conversion Based on New Paper 1 Syllabus for 2021
  
  Dr. Manishika Jain- Join online Paper 1 intensive course. Includes tests and expected questions.
  
  ## 1՚S & 2՚S Complement
  
  ### Convert to Binary: 2432 (Unsigned)
  
  Ans: 100110000000
  
  2048,256, 128
  
  Check if number is even its lsb would be 0 else would be 1
  
  ### Convert to Decimal: 11011001 (Unsigned)
  
  Ans: 11011001 = 217
  
  2048,256, 128
  
  Check if number is even its lsb would be 0 else would be 1
  
  ### The Negatives! !
  
  1. Signed Magnitude (5 bit machine)
  2. 1՚s Complement (5 bit machine)
  3. 2՚s Complement (5 bit machine)
  
  -5 Singed magnitude- 10101,1՚s Complement: 11010,2՚s complement: 11011.
  
  10101 signed magnitude:-5,1՚s Complement:-10,2՚s Complement -11
  
  2՚s Complement = 1՚s Complement + 1
  
  Negative numbers always have 1 in MSB!
  
  In all numbers + ve remain the same as unsigned
  
  ### The Negatives: Signed Magnitude
  
  -5 Singed magnitude: 10101
  
  -15 Singed magnitude: 11111
  
  11011:-11
  
  ### 01011: 11 the Negatives: 1՚S Complement
  
  -5 1՚s Complement: 11010 (Need machine
  
  width- guess from choices)
  
  -15 1՚s Complement: 10000 (More width would produce more 1՚s)
  
  11011:-4 (MSB is one so negative number, complement and find answer) If no 1 in MSB then simply write 11
  
  01011: 11 (Same as unsigned)
  
  ## The Negatives: 2՚S Complement
  
  -5 2՚s Complement: 11011 (Need machine width- guess from choices) (Add one to 1՚s Complement only for negative numbers)
  
  -15 2՚s Complement: 10001 (More width would produce more 1՚s)
  
  11011:-5 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 11
  
  11110:-2 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 14
  
  01011: 11 (Same as unsigned)
  
  ### Next Class
  
  -5 2՚s Complement: 11011 (Need machine width- guess from choices) (Add one to 1՚s Complement only for negative numbers)
  
  -15 2՚s Complement: 10001 (More width would produce more 1՚s)
  
  11011:-5 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 11
  
  11110:-2 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 14
  
  01011: 11 (Same as unsigned)
  
  Developed by:
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a series of binary to decimal conversion examples and explanations, including signed and unsigned numbers, 1's complement, and 2's complement. It includes both questions and their corresponding answers.
  
  Label: multiple-question-and-answer