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Questions and Answers
What is the largest integer that can be represented in an unsigned integer representation for n bits?
What is the largest integer that can be represented in an unsigned integer representation for n bits?
- $2^n$
- $n^2$
- $2^{n+1}$
- $2^n - 1$ (correct)
In the truth table of the OR operation, what condition results in an output of 1?
In the truth table of the OR operation, what condition results in an output of 1?
- At least one input is 1 (correct)
- Only one input is 0
- Both inputs are 1
- Both inputs are 0
If n is 5, what is the maximum value that can be represented in an unsigned integer format?
If n is 5, what is the maximum value that can be represented in an unsigned integer format?
- 25
- 32
- 31 (correct)
- 30
In a binary OR operation with inputs of 1 and 0, what will the output be?
In a binary OR operation with inputs of 1 and 0, what will the output be?
Which of the following statements best describes the behavior of the OR operation in binary logic?
Which of the following statements best describes the behavior of the OR operation in binary logic?
What is the result of the expression B > A when B is less than A?
What is the result of the expression B > A when B is less than A?
If B equals A, what will the result of the expression B > A be?
If B equals A, what will the result of the expression B > A be?
Which of the following scenarios would evaluate the expression B > A to 1 (True)?
Which of the following scenarios would evaluate the expression B > A to 1 (True)?
How does the truth value of B > A change when B is significantly larger than A?
How does the truth value of B > A change when B is significantly larger than A?
What is the significance of the truth table for the expression B > A?
What is the significance of the truth table for the expression B > A?
What were the early computers primarily constructed from?
What were the early computers primarily constructed from?
How are vacuum tubes described in the context of early computer designs?
How are vacuum tubes described in the context of early computer designs?
Which of the following statements is true about early computers?
Which of the following statements is true about early computers?
What classification do vacuum tubes fall under in early computer technology?
What classification do vacuum tubes fall under in early computer technology?
Which technology did NOT play a role in the design of early computers?
Which technology did NOT play a role in the design of early computers?
What is the binary representation of the decimal number 125?
What is the binary representation of the decimal number 125?
Which step is necessary to convert the decimal number 125 to binary?
Which step is necessary to convert the decimal number 125 to binary?
When converting the decimal number 125 to binary, how many bits would you need?
When converting the decimal number 125 to binary, how many bits would you need?
What is the highest power of 2 less than or equal to 125?
What is the highest power of 2 less than or equal to 125?
In the binary system, what is the decimal value of the binary number 1111101?
In the binary system, what is the decimal value of the binary number 1111101?
What does the acronym ENIAC stand for?
What does the acronym ENIAC stand for?
Which numerical system did ENIAC attempt to utilize for data representation?
Which numerical system did ENIAC attempt to utilize for data representation?
What was one of the primary innovations of the ENIAC?
What was one of the primary innovations of the ENIAC?
What type of calculations was ENIAC primarily designed to execute?
What type of calculations was ENIAC primarily designed to execute?
Which of the following best describes a limitation of early computers like ENIAC?
Which of the following best describes a limitation of early computers like ENIAC?
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Study Notes
Binary Representation
- The largest integer representable with n bits is 2^n - 1. This is because the first bit represents the sign, so it leaves (n-1) bits for the number.
Logical Operations
- The OR operation results in 1 (True) if at least one of the inputs is 1 (True).
ENIAC
- The ENIAC (Electronic Numerical Integrator and Computer) used vacuum tubes for processing data.
Decimal to Binary Conversion
- To convert a decimal number to binary, you can use the repeated division method.
- Divide the decimal number by 2.
- The remainder is the least significant bit of the binary representation.
- Repeat steps 1 and 2 with the quotient until the quotient is zero.
- The remainders, read from bottom to top, form the binary representation.
Example: Decimal to Binary Conversion
- Converting 125 to binary:
- 125 / 2 = 62 (remainder 1)
- 62 / 2 = 31 (remainder 0)
- 31 / 2 = 15 (remainder 1)
- 15 / 2 = 7 (remainder 1)
- 7 / 2 = 3 (remainder 1)
- 3 / 2 = 1 (remainder 1)
- 1 / 2 = 0 (remainder 1)
- Therefore, the binary representation of 125 is 1111101.
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