CS: Binary Arithmetic: Adding and Subtracting in Base 2
Practice binary sums, differences, carries, and borrows
CS: Binary Arithmetic: Adding and Subtracting in Base 2
Practice binary sums, differences, carries, and borrows
CS - Grade 6-8
- 1
Add the binary numbers 101 and 11. Show the numbers lined up by place value.
Pad the shorter number with a zero on the left: 011.
The sum is 1000 in binary. Lining up the numbers gives 101 plus 011, which equals 1000. - 2
Add the binary numbers 1101 and 1010.
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. - 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?
Think of 10 in binary as two in decimal.
In binary, 1 plus 1 equals 10, so you write 0 in the current column and carry 1 to the next column. - 4
Add all three binary numbers: 1011 + 110 + 1.
Line them up as 1011, 0110, and 0001 before adding.
The sum is 10010 in binary. The decimal values are 11, 6, and 1, which add to 18, and 18 is 10010 in binary. - 5
Subtract the binary numbers 1010 - 11. Show any borrowing you use.
Pad 11 as 0011 so the place values match.
The difference is 111 in binary. Lining up the numbers gives 1010 minus 0011, which equals 0111. - 6
Subtract 10000 - 1 in binary.
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. - 7
Find the sum: 1001 + 0110.
Check each column from right to left.
The sum is 1111 in binary. The decimal values are 9 and 6, and their sum is 15, which is 1111 in binary. - 8
A student writes 111 + 1 = 1111 in binary. Explain the mistake and give the correct sum.
Adding 1 to 111 causes carries through all three 1s.
The statement is incorrect because 111 in binary is 7 in decimal, and 7 plus 1 is 8. The correct binary sum is 1000. - 9
Add 1111 + 0001 in binary.
The sum is 10000 in binary. Each 1 plus the carry becomes 0 with a carry until a new leftmost 1 is created. - 10
A robot has 1010 energy packets and receives 0111 more. How many energy packets does the robot have now in binary?
You can check by converting 1010 to 10 and 0111 to 7 in decimal.
The robot has 10001 energy packets in binary. The values 1010 and 0111 add to 10001. - 11
A folder contains 1100 files. A program deletes 0101 files. How many files remain in binary?
There are 0111 files remaining in binary. The subtraction 1100 minus 0101 equals 0111. - 12
Find the missing addend: 1011 + ____ = 10000.
Think of this as a subtraction problem: 10000 minus 1011.
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. - 13
Subtract 1001 - 0101 in binary.
Borrow when a top bit is 0 and the bottom bit is 1.
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. - 14
Subtract 100000 - 1011 in binary. Show your final answer without unnecessary leading zeros.
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. - 15
Evaluate the binary expression (10100 - 0111) + 10. Give the final answer in binary.
Do the subtraction first because it is inside the parentheses.
The final answer is 1111 in binary. First, 10100 minus 0111 equals 1101, and then 1101 plus 10 equals 1111.