Week 2 Flashcards
What is the base-B arithmetic addition rule?
If ei >= B, add 1 to ei+1 and set ei = xi + yi - B.
What are the binary addition rules?
0+0=0, 1+0=1, 1+1=10 (0 with carry 1), 1+1+1=11 (1 with carry 1).
How is binary subtraction performed when ei < 0?
Borrow 1 from xi+1 and include it in xi.
What does the complement (NOT) operation do in binary?
Switch 0 to 1 and vice versa.
What does the conjunction (AND) operation do?
1 if both bits are 1, otherwise 0.
What is the disjunction (OR) operation?
1 if at least one of the two bits is 1, otherwise 0.
What is the exclusive disjunction (XOR) operation?
1 if exactly one of the two bits is 1, otherwise 0.
How does left bit shifting work?
Shifts bits to the left, introducing zeroes, effectively multiplying by 2^n.
How does signed right bit shifting work?
Shifts bits to the right, repeating the most significant bit.
What is bit masking used for?
Manipulating specific bits within an integer using AND, OR, XOR, and NOT operations.
What is the sum expanded representation for base-10?
Calculate as d_n * 10^n + d_(n-1) * 10^(n-1) + … + d_0 * 10^0.
What is Horner’s rule used for?
A recursive method to convert numbers to base-10.
How do you convert base-10 to another base using the repeated division method?
Divide repeatedly by the base, and reverse the sequence of remainders.
What is the largest power method for base conversion?
List powers of the base, find the largest fitting value, and subtract iteratively.
What is the process to convert between two arbitrary bases?
Convert from the source base to base-10, then from base-10 to the target base.
Why do programmers prefer “hex” as a shorthand for binary?
Programmers prefer hexadecimal because each hex digit represents exactly 4 binary bits, making it much more compact and easier to read or write large binary values
