CALCU-binary arithmatic: 110111110 + 011100011

binary arithmatic: 110111110 + 011100011

Solution by Steps

step 1

Convert the binary numbers to decimal to check the sum

step 2

The binary number 110111110 converts to the decimal number 222

step 3

The binary number 011100011 converts to the decimal number 227

step 4

Add the decimal numbers: 222 + 227

step 5

The sum of the decimal numbers is 449

step 6

Convert the decimal sum 449 back to binary

step 7

The binary representation of 449 is 110111001

Answer

110111110 + 011100011 = 110111001

Key Concept

Binary Addition

Explanation

To perform binary addition, align the numbers by their least significant bit and add each column, carrying over as you would in decimal addition when a column sums to 2 (10 in binary). The asksia-ll calculator provided the correct sum in binary.

calculate binary 010110010 + 110011101 without converting to decimals

Solution by Steps

step 1

To calculate the binary sum of 010110010 and 110011101, we align the numbers and add them starting from the rightmost bit

step 2

Add the rightmost bits:

0 + 1 = 1

step 3

Move to the next bit:

1 + 0 = 1

step 4

Continue with the next bit:

0 + 1 = 1

step 5

Next bit:

1 + 1 = 10

. This is

0

in the current column with a carryover of

1

step 6

With the carryover:

1 (carry) + 1 + 0 = 10

. Write down

0

and carry over

1

step 7

Next bit with carryover:

1 (carry) + 0 + 1 = 10

. Write down

0

and carry over

1

step 8

Continue:

1 (carry) + 1 + 0 = 10

. Write down

0

and carry over

1

step 9

Next bit:

1 (carry) + 0 + 1 = 10

. Write down

0

and carry over

1

step 10

Next bit:

1 (carry) + 1 + 1 = 11

. Write down

1

and carry over

1

step 11

For the leftmost bit, add the carryover:

1 (carry) + 0 + 1 = 10

. Write down

0

and carry over

1

step 12

Place the carryover at the leftmost position to complete the sum:

1

+ the result from the previous steps

Answer

010110010 + 110011101 = 1001101111

Key Concept

Binary Addition

Explanation

In binary addition, we add bit by bit from right to left, carrying over any value that exceeds 1 to the next left bit. The sum of two binary digits follows the rules:

0 + 0 = 0

,

0 + 1 = 1

,

1 + 0 = 1

, and

1 + 1 = 10

, where

10

in binary represents

2

in decimal, requiring a carryover to the next higher bit.

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