1. Binary

3. Binary digit = a Bit
All Computers store programs and data as binary, therefore all data that is input into a computer must be converted into binary (machine code) before it can be processed by the computer.
Bit is a single binary unit or 1 is stored. (off or on)
A byte is a collection of 8 bits so therefore a combination of eight 0’s or 1’s combine for a byte.
E.g
A nibble is 4 bits, e.g. 0111

4. Denary We are used to counting in denary which allows the range 0-9
The table below demonstrates how a byte binary number represents a denary value.
Denary
Binary Data
128 64 32 16 8 4 2 1 7 60
129
140
151
166
255

5. Converting denary to binary
As stated earlier for the computer to understand the data it must convert the denary to a binary value.
Example
Converting 47 to binary. Hint: work from the left.
128 64 32 16 8 4 2 1
= 47

6. Converting denary to binary
Convert the following denary values to binary:
1. 27
128 64 32 16 8 4 2 1
2. 38
3. 165

7. Converting denary to binary
1. What is the largest denary value you can make in binary?
128 64 32 16 8 4 2 1

8. The largest value that may be stored in a Byte (8 bits) is shown below
128 64 32 16 8 4 2 1
255

9. Converting binary to denary.
Convert the following binary values to denary:
128 64 32 16 8 4 2 1

10. Adding binary Adding binary example. Notes: 0 + 0 = 0 1 + 0 = 11
Notes:
0 + 0 = 0
1 + 0 = 1
1 + 1 = 10 so write 0 carry 1. binary 1 + binary 1 = binary 2.
= 11 so write 1 carry 1. binary 1 + binary 1 + binary 1= binary 3.

11. Adding binary – attempt the following
Attempt the following binary addition. (9+5) 1
Attempt the following binary addition. (7+5) 1

12. Adding binary – attempt the following
Attempt the following binary addition. (9+5) 1
Attempt the following binary addition. (7+5) 1

13. Overflow error
When dealing with a byte (8 bits) the largest number we can store is 255.
If we add two numbers that combine for a total of more than 255 then an overflow error would occur in this case.
E.g = This could not be stored in binary within a byte.
Overflow
128 64 32 16 8 4 2 1
200
178+

14. Overflow
Overflow
128 64 32 16 8 4 2 1
The overflow digit cannot be stored so the answer becomes
= 122!
Overflow errors happen when the largest number that a register can hold is exceeded. The number of bits that it can handle is called the word size.
Most CPUs use a much bigger word size than 8 bits. Many PCs have a 64-bit CPU. A 64-bit CPU can handle numbers larger than 18 quintillion (18,446,744,073,709,551,615 to be precise).

15. Past Paper Questions

16. Past Paper Questions

17. Past Paper Questions