Binary
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 - 0 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. 00110011 A nibble is 4 bits, e.g. 0111
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
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 32+8+4+2+1 = 47
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
Converting denary to binary 1. What is the largest denary value you can make in binary? 128 64 32 16 8 4 2 1
The largest value that may be stored in a Byte (8 bits) is shown below 128 64 32 16 8 4 2 1 255
Converting binary to denary. Convert the following binary values to denary: 1. 00101101 128 64 32 16 8 4 2 1 2. 10110001 3. 0011
Adding binary Adding binary example. Notes: 0 + 0 = 0 1 + 0 = 1 1 Notes: 0 + 0 = 0 1 + 0 = 1 1 + 1 = 10 so write 0 carry 1. binary 1 + binary 1 = binary 2. 1 + 1 + 1 = 11 so write 1 carry 1. binary 1 + binary 1 + binary 1= binary 3.
Adding binary – attempt the following Attempt the following binary addition. (9+5) 1 Attempt the following binary addition. (7+5) 1
Adding binary – attempt the following Attempt the following binary addition. (9+5) 1 Attempt the following binary addition. (7+5) 1
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. 200 + 178 = 378. This could not be stored in binary within a byte. Overflow 128 64 32 16 8 4 2 1 200 178+
Overflow Overflow 128 64 32 16 8 4 2 1 The overflow digit cannot be stored so the answer becomes 01111010 = 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).
Past Paper Questions
Past Paper Questions
Past Paper Questions