Modular Arithmetic and Number Representation

The video tutorial covers integer representations and algorithms, focusing on base expansions such as binary, octal, and hexadecimal. It explains how different bases affect the length of number representations and provides algorithms for converting numbers between bases. The tutorial also delves into modular arithmetic, including efficient methods for modular exponentiation, and discusses algorithm complexity.

What is the base b expansion of a number?

• A technique to simplify complex numbers.

• A representation of a number using powers of b.

• A method to convert numbers to binary.

• A way to express numbers using only zeros and ones.

How is the number 534 represented in base 10?

• Five hundreds, three tens, and four ones.

• Five tens, three hundreds, and four ones.

• Five ones, three tens, and four hundreds.

• Five hundreds, four tens, and three ones.

What is the hexadecimal representation of the number 43,862?

• 5AB6

• AB56

• A5B6

• B5A6

What is the first step in converting a number from base 10 to another base?

• Add the number to the new base.

• Multiply the number by the new base.

• Subtract the new base from the number.

• Divide the number by the new base.

What is the octal expansion of the number 12,321?

• 30041

• 12321

• 32104

• 41230

How many binary digits are needed to represent an octal digit?

• Three

• Five

• Two

• Four

What is the brute force method for division?

• Subtracting the divisor repeatedly from the dividend.

• Dividing the dividend by the divisor directly.

• Multiplying the divisor by the dividend.

• Adding the divisor repeatedly to the dividend.

What is the remainder when -19 is divided by 4?

• 0

• 1

• 3

• 2

What is the purpose of modular exponentiation?

• To compute powers efficiently under a modulus.

• To find the greatest common divisor.

• To convert numbers to binary.

• To simplify division operations.

What is the result of 3 to the 11th power mod 5?

• 4

• 2

• 1

• 3