Binary Builder
Doing sums in binary: adding numbers column by column with a carry, spotting overflow when a result will not fit, and using binary shifts left and right to multiply and divide by powers of two.
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Sums in ones and zeros
Computers do all their maths in binary, using only 0 and 1. Once you know a few rules, adding binary numbers and shifting their bits is quick. This module works through binary addition and the carry, what happens when a result overflows, and how shifting the bits left or right multiplies or divides the value.
Binary words to know
Learn these before you add a single bit.
Left shift against right shift
Both move the bits, but in opposite directions with opposite effects.
Add column by column, then shift
In the exam, work binary addition column by column from the right, and remember the rules: 0 plus 0 is 0, 0 plus 1 is 1, and 1 plus 1 is 0 carry 1. If the total spills past the eighth bit into a ninth you do not have, that is overflow. For a shift, move every bit the given number of places: a left shift multiplies and a right shift divides, by two for each place moved.
Match the term
- binary addition
- carry
- overflow
- binary shift
- adding numbers written in binary
- a 1 passed to the next column
- when the result will not fit in the bits
- moving all the bits left or right
Match the effect
- a left shift of one place
- a right shift of one place
- adding 1 and 1 in a column
- needing a ninth bit in an 8-bit sum
- doubles the value
- halves the value
- gives 0 and carries 1
- causes an overflow
What is 1 plus 1 in binary?
When adding a binary column, what is 1 plus 1?
- 0 with a carry of 1
- 2
- 1 with no carry
- 0 with no carry
True about binary arithmetic
Select the TWO true statements about binary arithmetic.
- A left shift multiplies a binary number by two for each place
- Overflow happens when a result needs more bits than are available
- In binary, 1 plus 1 equals 2 with no carry
- A right shift multiplies the number
Shift and multiply
A binary number worth 6 is shifted one place to the left. A single left shift doubles the value. What is the new value as a decimal number?
Order the addition
Put the steps of adding two binary numbers in order, earliest first.
- Line up the two numbers by their columns
- Start adding from the right-hand column
- Carry a 1 to the next column when needed
- Read off the answer and check for overflow
Complete the rules
Adding numbers written in binary is binary _____. When a column adds to more than one, you _____ a 1 to the next column. If the result needs more bits than there are, this is _____. Moving all the bits left or right is a binary _____.
Spot the true binary facts
Tap the TWO true statements about binary arithmetic.
- a left shift multiplies the value by two
- 1 plus 1 gives 0 with a carry of 1
- a right shift multiplies the value
- overflow means the answer fits easily
Work it out
Read each case and choose the best answer.
- You add two 8-bit numbers and the answer needs a ninth bit that does not exist. What has happened?
- You shift a binary number one place to the left. What happens to its value?
- A binary column adds up to 1 plus 1. What do you write and do?
Explain binary arithmetic
Explain how to add binary numbers and how a binary shift changes a value.
- Explain the rules for adding a binary column, including the carry
- Explain what overflow is
- Explain what a left shift and a right shift do to a value