10 Questions
What is the primary reason why decimal numbers need to be converted to binary?
Computers only understand binary language
What is the first step in converting a decimal number to binary?
Divide the decimal number by 2
What is the purpose of taking the remainder and dividing it by 2 again in the decimal to binary conversion process?
To repeat the process until the result is 0
What is the final step in converting a decimal number to binary using the division method?
Read the binary digits from bottom to top
What is the purpose of using a binary conversion table?
To convert decimal numbers to binary quickly
What is the process of creating tiny computers and components less than 100 nanometers in size?
Nanotechnology
What is the function of the Bus Interface Unit?
Allows the core to communicate with other CPU components
What is the term for the series of operations involved in the execution of a single machine level instruction?
Machine Cycle
What is the term for computers that use light to perform digital computations?
Optical Computing
What is the term for the ability to process one trillion floating-point operations per second?
Tera-Scale Computing
Study Notes
Decimal to Binary Conversion
Why Convert Decimal to Binary?
- Computers only understand binary language (0s and 1s)
- Decimal numbers are used by humans, but computers need binary to process information
Steps to Convert Decimal to Binary
-
Divide the decimal number by 2
- If the result is a whole number, write down 0
- If the result is a decimal, write down 1
-
Take the remainder and divide it by 2 again
- Repeat step 1 until the result is 0
-
Read the binary digits from bottom to top
- The resulting sequence of 0s and 1s is the binary equivalent of the decimal number
Examples
- Convert 12 to binary:
- 12 ÷ 2 = 6 (0)
- 6 ÷ 2 = 3 (0)
- 3 ÷ 2 = 1.5 (1)
- 1 ÷ 2 = 0.5 (1)
- Binary equivalent: 1100
- Convert 25 to binary:
- 25 ÷ 2 = 12.5 (1)
- 12 ÷ 2 = 6 (0)
- 6 ÷ 2 = 3 (0)
- 3 ÷ 2 = 1.5 (1)
- 1 ÷ 2 = 0.5 (1)
- Binary equivalent: 11001
Shortcut: Using a Binary Conversion Table
- Create a table with powers of 2 (2^0, 2^1, 2^2, ...)
- Find the decimal number in the table and write down the corresponding binary digits
- Combine the binary digits to get the binary equivalent of the decimal number
Why Convert Decimal to Binary?
- Computers only understand binary language, consisting of 0s and 1s
- Decimal numbers are used by humans, but computers need binary to process information
Steps to Convert Decimal to Binary
- Divide the decimal number by 2, and write down 0 if the result is a whole number, or 1 if the result is a decimal
- Take the remainder and divide it by 2 again, repeating step 1 until the result is 0
- Read the binary digits from bottom to top to get the binary equivalent of the decimal number
Examples of Decimal to Binary Conversion
- 12 in decimal is equal to 1100 in binary
- 25 in decimal is equal to 11001 in binary
Shortcut: Using a Binary Conversion Table
- Create a table with powers of 2 (2^0, 2^1, 2^2,...)
- Find the decimal number in the table and write down the corresponding binary digits
- Combine the binary digits to get the binary equivalent of the decimal number
Learn how to convert decimal numbers to binary language that computers understand. Understand the steps involved in the conversion process.
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