Binary Addition Questions and Rules Quiz with Flashcards

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Questions and Answers

What is a common symbol used in binary representation?

2 (correct)

When adding in binary, what happens if you run out of digits?

You add another bit to continue the addition

You carry over the remaining digit to the final answer (correct)

You add a 1 to the rightmost bit and continue

You ignore the carry and stop adding

In binary addition, what is done when the sum exceeds two digits?

The sum is discarded

The sum is truncated to fit in a single digit

A carry is generated to the next bit position (correct)

The sum is divided by 2

What is the binary representation of the decimal number 10?

1010 Signup and view all the answers

In binary addition, what does it mean to 'Add with Carry'?

Consider any carry from the previous addition Signup and view all the answers

When adding two binary numbers, what do we do if the sum is greater than 1 for a single bit?

Generate a carry to the next higher bit Signup and view all the answers

What is the main difference between binary and decimal number systems?

Binary system uses digits from 0 to 1, while decimal system uses digits from 0 to 9 Signup and view all the answers

Why is it necessary to have carry digits in binary addition?

To indicate that the sum is greater than the highest single digit in binary Signup and view all the answers

What happens when you compute 1 + 1 in binary?

A carry of 1 is needed Signup and view all the answers

Why do we represent the result of 10 as two separate digits in binary addition?

Because it exceeds the limit of single binary digit Signup and view all the answers

What does the highest digit in binary represent?

1 Signup and view all the answers

Why do we need to be careful with carrying and borrowing in binary addition and subtraction?

To avoid errors due to running out of available digits while adding or subtracting Signup and view all the answers

What is the result of 25 - 123 using 8-bit 2’s complement?

01100001 Signup and view all the answers

What is the 1's complement of the subtrahend in the subtraction example provided?

10000100 Signup and view all the answers

Which rule of binary addition states '0 - 1 = 1 (borrow 1 from the more significant bit)'?

'1-0=1' Signup and view all the answers

What does 'No carry implies negative number' mean in binary arithmetic?

The result is negative Signup and view all the answers

How do we obtain the value after performing a binary subtraction when there is no carry?

Performing a 2's complement of the result Signup and view all the answers

What is the rule of binary multiplication stating '1 x 1 = 1 (no carry or borrow bits)'?

'1x1=1' Signup and view all the answers

Study Notes

Binary Representation

Non-negative integers are represented in Binary with Most Significant Bit (MSB) and Least Significant Bit (LSB)
Binary representation uses only 2 symbols: 0 and 1

Binary Addition

Binary addition is similar to decimal addition, but with 2 digits only (0 and 1)
Carry and borrow rules apply, with careful handling of digits
Example: 5 + 7 in binary form (1012 + 1112) with carry and borrow

Binary Subtraction

Binary subtraction is similar to decimal subtraction
Example: 25 - 123 using 8-bit 2's complement representation

Binary Arithmetic Rules

Rules of Binary Addition:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0 (carry 1 to the next more significant bit)
Rules of Binary Subtraction:
- 0 - 0 = 0
- 0 - 1 = 1 (borrow 1 from more significant bit)
- 1 - 0 = 1
- 1 - 1 = 0
Rules of Binary Multiplication:
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1 (no carry or borrow bits)

Binary Multiplication

Binary multiplication follows the same process as decimal multiplication
Multiply each digit of the second number by the first whole number, then add them, shifting each resulting multiplication one digit to the left.

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Description

Test your knowledge on binary addition rules and number representation. Learn how to add binary numbers and how to deal with carrying over digits in multi-digit additions.