CS: Binary Arithmetic: Adding and Subtracting in Base 2 Worksheet

Question 1

Add the binary numbers 101 and 11. Show the numbers lined up by place value.

Accepted Answer

The sum is 1000 in binary. Lining up the numbers gives 101 plus 011, which equals 1000.

Question 2

Add the binary numbers 1101 and 1010.

Accepted Answer

The sum is 10111 in binary. In decimal, 1101 is 13 and 1010 is 10, so the total is 23, which is 10111 in binary.

Question 3

In binary addition, what do you write in the current column when you add 1 plus 1, and what do you carry to the next column?

Accepted Answer

In binary, 1 plus 1 equals 10, so you write 0 in the current column and carry 1 to the next column.

Question 4

Add all three binary numbers: 1011 + 110 + 1.

Accepted Answer

The sum is 10010 in binary. The decimal values are 11, 6, and 1, which add to 18, and 18 is 10010 in binary.

Question 5

Subtract the binary numbers 1010 - 11. Show any borrowing you use.

Accepted Answer

The difference is 111 in binary. Lining up the numbers gives 1010 minus 0011, which equals 0111.

Question 6

Subtract 10000 - 1 in binary.

Accepted Answer

The difference is 1111 in binary. Since 10000 is 16 in decimal and 1 is subtracted, the result is 15, which is 1111 in binary.

Question 7

Find the sum: 1001 + 0110.

Accepted Answer

The sum is 1111 in binary. The decimal values are 9 and 6, and their sum is 15, which is 1111 in binary.

Question 8

A student writes 111 + 1 = 1111 in binary. Explain the mistake and give the correct sum.

Accepted Answer

The statement is incorrect because 111 in binary is 7 in decimal, and 7 plus 1 is 8. The correct binary sum is 1000.

Question 9

Add 1111 + 0001 in binary.

Accepted Answer

The sum is 10000 in binary. Each 1 plus the carry becomes 0 with a carry until a new leftmost 1 is created.

Question 10

A robot has 1010 energy packets and receives 0111 more. How many energy packets does the robot have now in binary?

Accepted Answer

The robot has 10001 energy packets in binary. The values 1010 and 0111 add to 10001.

Question 11

A folder contains 1100 files. A program deletes 0101 files. How many files remain in binary?

Accepted Answer

There are 0111 files remaining in binary. The subtraction 1100 minus 0101 equals 0111.

Question 12

Find the missing addend: 1011 + ____ = 10000.

Accepted Answer

The missing addend is 0101 in binary. Since 10000 is 16 in decimal and 1011 is 11, the missing value is 5, which is 0101 in binary.

Question 13

Subtract 1001 - 0101 in binary.

Accepted Answer

The difference is 0100 in binary. In decimal, 1001 is 9 and 0101 is 5, so the difference is 4, which is 0100 in binary.

Question 14

Subtract 100000 - 1011 in binary. Show your final answer without unnecessary leading zeros.

Accepted Answer

The difference is 10101 in binary. In decimal, 100000 is 32 and 1011 is 11, so the difference is 21, which is 10101 in binary.

Question 15

Evaluate the binary expression (10100 - 0111) + 10. Give the final answer in binary.

Accepted Answer

The final answer is 1111 in binary. First, 10100 minus 0111 equals 1101, and then 1101 plus 10 equals 1111.

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