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Computing Academy GCSE Computer Science

The column values are 10

The column values are 10 times the value in the previous column moving from right to left. This is called the base 10 system, or the denary or decimal system. Computers do not use the decimal system. They use a system based on just two numbers: 1 and 0. This is called the binary or base 2 system. In the same way that we multiply by 10 in the denary system to move across from right to left, when using the binary system, multiplying by 2 moves across to the left. See how we move across from right to left with 1, 2, 4, 8, 16, 32, 64, 128. 128 64 32 16 8 4 2 1 Binary Units When using the denary (base 10) system we assign certain numbers special names, for example 10 × 10 × 10 is 1000 which we call a thousand. 1 thousand multiplied by 1 thousand is called 1 million etc. Binary also has some special names to refer to certain values. The basic unit is 0 or 1 – this is a binary digit or bit. When talking about storing and transferring data within a computer system we talk about ‘bits’ and ‘bytes’. ‘Bit’ is short for ‘Binary Digit’ and a byte contains 8 bits. A ‘nibble’ is half of one byte (4 bits). 57

Binary to Denary 128 64 32 16 8 4 2 1 0 0 1 0 1 0 0 1 In the above example, we can say that we have no 128s, no 64s, 1 lot of 32, no 16s, 1 lot of 8, no 4s, no 2s and 1 lot of 1. So we have 32 + 8 + 1 = 41. 00101001 is therefore the binary representation or equivalent of the decimal number 41. Here are some more numbers represented using the binary system. 128 64 32 16 8 4 2 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 The first number has a ‘1’ for 32 and everything else has a ‘0’, so 00100000 is binary for 32. 0 1 0 1 0 0 0 1 The second number has a ‘1’ for 64 and a ‘1’ for 16 and a ‘1’ for 1, so we have 64 + 16 + 1 = 81, so 01010001 is binary for 81. 0 0 1 0 1 1 0 1 The third binary number is 00101101 so there is a ‘1’ for 32, 8, 4 and 1. 32 + 8 + 4 + 1 = 45, so 00101101 is binary for 45! 58

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