Cambridge IGCSE Computer Science

## Why computers use binary A computer is built from electronic circuits that have two reliable states, on and off (or high and low voltage). A single circuit therefore stores one **binary digit**, or **bit**, which is 0 or 1. Every kind of data a computer handles, whether numbers, text, images, sound or the instructions of a program, has to be converted into patterns of bits before it can be processed. Logic gates work on those bits, and registers inside the processor hold them. ## Three number systems Each system is defined by its **base**, which is the number of different digits it uses and the value each place is worth a power of. | System | Base | Digits used | |---|---|---| | Denary (decimal) | 10 | 0 to 9 | | Binary | 2 | 0 and 1 | | Hexadecimal | 16 | 0 to 9 and A to F | In hexadecimal, A to F stand for the values 10 to 15, because a single digit has to be able to hold sixteen different values. The place values in denary are powers of ten (1, 10, 100, 1000), in binary they are powers of two, and in hexadecimal they are powers of sixteen. For an 8-bit binary number the place values from left to right are: | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | |---|---|---|---|---|---|---|---| The leftmost bit is the **most significant bit** (MSB), because it is worth the most, and the rightmost is the **least significant bit** (LSB). A 16-bit number extends the same pattern to the left with 32768, 16384, 8192, 4096, 2048, 1024, 512 and 256. ## Binary to denary Write the place values…