8 Questions
What is the decimal equivalent of the hexadecimal numeral A?
10
What is the general formula for finding the decimal equivalent of a hexadecimal number?
( hexadecimal number ) × 16^n where n is the position of the digit
When adding hexadecimal numbers, what happens if the sum of a column exceeds 15?
You convert the sum to hexadecimal and carry over to the next column
What is the purpose of borrowing in hexadecimal subtraction?
To treat the borrowed amount as 16 in decimal
How do you multiply hexadecimal numbers?
By multiplying each digit of the bottom number by the entire top number
What is the final step in hexadecimal multiplication?
Add all the products together, converting to hexadecimal if necessary
How do you perform hexadecimal division?
By dividing the dividend by the divisor to find the quotient
What is the base of the hexadecimal number system?
16
Study Notes
Hexadecimal Number Systems
- Hexadecimal is a base-16 number system comprising 16 symbols: 0-9, A, B, C, D, E, and F.
- The numerals A, B, C, D, E, and F have decimal equivalents of 10, 11, 12, 13, 14, and 15 respectively.
Base 16 (Hexadecimal) Representation
- Hexadecimal is a base-16 numbering system that uses 16 distinct symbols: 0-9, and A-F, where A=10, B=11, C=12, D=13, E=14, and F=15.
Operations in Hexadecimal System
Addition
- To add hexadecimal numbers, write them down vertically, aligning them by their rightmost digits.
- Add the numbers column by column, starting from the right.
- If the sum of a column exceeds 15, convert it to hexadecimal and carry over to the next column.
Subtraction
- To subtract hexadecimal numbers, write down the numbers with the larger one on top.
- Subtract the numbers column by column, starting from the right.
- If you cannot subtract a smaller digit from a larger digit, borrow from the next left column, treating the borrowed amount as 16 in decimal.
Multiplication
- Hexadecimal multiplication is similar to decimal multiplication:
- Multiply each digit of the bottom number by the entire top number.
- Write each resulting product one row lower than the previous, shifted one place to the left.
- Add all the products together, converting to hexadecimal if necessary.
Division
- Hexadecimal division is performed like decimal division:
- Divide the dividend by the divisor to find the quotient.
- Write down the remainder if any.
- Continue the process with the next digit of the dividend.
General Rules
- When performing operations in hexadecimal, remember that you're working in a base-16 system, so each column can only contain digits from 0 to F.
- Carrying or borrowing operates on multiples of 16.
Learn about the basics of hexadecimal number system, including its representation, symbols, and operations such as addition.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
