Flashcards on Addition and subtraction in the binary system
Binary Addition & Subtraction: A Guide to Computer Arithmetic
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Binary Number Operations
12 cards
Card 1
Question: What is the foundational language of all modern digital computers and electronic devices?
Answer: The binary number system, or base-2 system.
Card 2
Question: How many digits does the binary system use and what are they?
Answer: Two digits: 0 and 1.
Card 3
Question: How is the decimal number 5 represented in binary, and what does each position signify?
Answer: 101₂. Each position in a binary number represents a power of two, similar to how each position in a decimal number represents a power of ten.
Card 4
Question: What are the basic rules for adding two binary digits (bits)?
Answer: 1. 0 + 0 = 0 2. 0 + 1 = 1 3. 1 + 0 = 1 4. 1 + 1 = 10₂ (0 with a carry of 1)
Card 5
Question: What happens when a carry is generated in binary addition?
Answer: It is added to the bits in the next column to the left.
Card 6
Question: What are the rules for adding three binary digits in a column (two original bits plus a carry-in)?
Answer: 1. 0 + 0 + 0 = 0 2. 0 + 0 + 1 = 1 3. 0 + 1 + 0 = 1 4. 0 + 1 + 1 = 10₂ (0 with a carry of 1) 5. 1 + 0 + 0 = 1 6. 1 + 0 + 1 = 10₂ (0 with a carry of 1)
Card 7
Question: Perform the binary addition: 1011₂ + 0101₂.
Answer: 10000₂
Card 8
Question: In binary addition, if you add 1011₂ (decimal 11) and 0101₂ (decimal 5), what is the step-by-step process for the rightmost (2⁰) and second (2¹) colum
Answer: Rightmost column (2⁰ position): 1 + 1 = 10₂. Write down 0, carry over 1. Second column (2¹ position): 1 (carry) + 1 + 0 = 10₂. Write down 0, carry ove
Card 9
Question: What is an 'overflow' in the context of binary number operations with a fixed number of bits?
Answer: An overflow occurs when the result of an arithmetic operation exceeds the maximum value that can be stored within the allocated number of bits.
Card 10
Question: Give an example of an overflow in a 4-bit unsigned binary system when adding two numbers.
Answer: Adding 1000₂ (decimal 8) and 1000₂ (decimal 8) results in 10000₂ (decimal 16). In a 4-bit system, the fifth bit (carry) is lost, and the result become