Contest Python: ACSL › Unit 1 — Computer Number Systems
Exercises: Unit 1 — Computer Number Systems
There are two kinds of exercises here, just as on an ACSL contest.
- Short-answer: work it out with pencil and paper and write one exact answer.
Write a number in a base without the small base subscript: if the question asks for base 8, the answer to "45 in base 8" is
55. Write hex digits as capital letters (2D, not2d), leave out leading zeros, and write fractions in lowest terms, such as5/8. - Programming: write a complete program that reads the input with
input()and prints exactly the output described. Save it as a.pyfile and run it from a terminal, typing the sample input or feeding it a file.
Each exercise is marked with the lowest ACSL division it belongs to. Do every exercise at or below your division. Exercises 1 to 9 are an Elementary practice test: no programming, only what Lesson 1 teaches. Exercises marked Challenge are extra practice for when you want more.
Exercise 1: Binary to Decimal
What is 10110₂ in base 10?
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 2: Octal to Decimal
What is 237₈ in base 10?
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 3: Binary to Octal
Write 110101101₂ in base 8.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 4: Binary to Hex
Write 1011110₂ in base 16.
How this is checked: Checked by comparing your answer with the expected answer, ignoring capital letters.
Answer format: A hexadecimal number: base-16 digits only, with capital letters A–F for the digits after 9 (as in `2D`), no base subscript and no leading zeros. Small letters are accepted too.
Exercise 5: Binary Addition
Find 1011₂ + 111₂. Write the answer in base 2.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 6: Octal Subtraction
Find 75₈ − 26₈. Write the answer in base 8.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 7: Which Is Largest?
Here are three numbers:
- 1111000₂
- 171₈
- 77₁₆
Which one is the largest? Write its value in base 10.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 8: How Much Green?
The colour #1E90FF is a bright sky blue.
How much green is in it?
Write the amount in base 10.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 9: Count the Ones
How many 1s are in the binary form of 173₁₀?
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 10: Octal to Hex
Write 5273₈ in base 16.
How this is checked: Checked by comparing your answer with the expected answer, ignoring capital letters.
Answer format: A hexadecimal number: base-16 digits only, with capital letters A–F for the digits after 9 (as in `2D`), no base subscript and no leading zeros. Small letters are accepted too.
Exercise 11: Into Base 7
Write 500₁₀ in base 7.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 12: Hex Subtraction
Find C04A₁₆ − 3B7F₁₆. Write the answer in base 16.
How this is checked: Checked by comparing your answer with the expected answer, ignoring capital letters.
Answer format: A hexadecimal number: base-16 digits only, with capital letters A–F for the digits after 9 (as in `2D`), no base subscript and no leading zeros. Small letters are accepted too.
Exercise 13: Times a Digit
Find 3547₈ × 6₈. Write the answer in base 8.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 14: The Inverse Colour
The inverse of a colour replaces each of its red, green and blue amounts by 255 minus that amount.
What is the inverse of #3C8FD2?
Write the answer as its six hex digits, without the #.
How this is checked: Checked by comparing your answer with the expected answer, ignoring capital letters.
Answer format: Six hex digits without the `#`, with capital letters A–F for the digits after 9 (as in `2D`). Small letters are accepted too.
Exercise 15: Digits in Another Base
The input is one line holding two integers, N and B.
Print N written in base B, then one space, then the sum of its digits as a base-10 number.
Digits above 9 are the letters A to F, and the letter's value (A = 10, …, F = 15) counts in the sum.
Constraints
0 <= N <= 10000002 <= B <= 16
Sample Input
500 7Sample Output
1313 8500 is 1313₇, and 1 + 3 + 1 + 3 = 8.
How this is checked: Checked by running your program on 5 test inputs (1 sample, 4 hidden) and comparing its output line by line.
Exercise 16: The Biggest Card
Each card holds a number and the base it is written in. Find the card with the largest value.
The first line holds N, the number of cards.
Each of the next N lines holds one card: the digits of the number (hex digits as capital letters), a space, and its base B.
Print the largest value, in base 10.
Constraints
1 <= N <= 502 <= B <= 16, and every digit on a card is a digit of that card's base.- Every value is between 0 and 1000000 in base 10.
Sample Input
3
101101 2
55 8
2F 16Sample Output
47The cards are worth 45, 45 and 47.
How this is checked: Checked by running your program on 4 test inputs (1 sample, 3 hidden) and comparing its output line by line.
Exercise 17: Double Palindromes
A palindrome reads the same forwards and backwards, such as 121 or 1001.
Some numbers are palindromes both in base 10 and in base 2: 9 is 9 in base 10 and 1001 in base 2.
The input is one line holding two integers, A and B.
Print how many whole numbers from A to B (including both) are palindromes in base 10 and in base 2.
Constraints
1 <= A <= B <= 100000
Sample Input
1 10Sample Output
5They are 1, 3, 5, 7 and 9 (in base 2: 1, 11, 101, 111 and 1001).
How this is checked: Checked by running your program on 5 test inputs (1 sample, 4 hidden) and comparing its output line by line.
Exercise 18: Octal Fraction
Write 0.34₈ as a base-10 fraction in lowest terms.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: A base-10 fraction in lowest terms, written with `/`, such as `5/8`.
Exercise 19: Hex Fraction
Write 0.A8₁₆ as a base-10 fraction in lowest terms.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: A base-10 fraction in lowest terms, written with `/`, such as `5/8`.
Exercise 20: A Fraction in Binary
Write 11/16 in base 2.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: A base-2 number with a point, such as `0.011`, written without the small base subscript.
Exercise 21: The Mystery Base
In some base b, the number 132, written in base b, is equal to 56₁₀. What is b? Write it in base 10.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number