How to do math in a computer? Mathematics is a crucial discipline, which cannot be overlooked, especially in the field of technology. Computers accurately perform mathematical calculations in binary form, which is quite different from what we use: the decimal numbering. Binary typically refers to a numbering system invented by Gottfried Leibniz. In this approach of numbering, a digit has only two possible states or values, i.e. 0 and 1. 0s denote OFF, false or low, and 1s indicate ON, true or high in a transistor. It allows the storage of numbers in a computing device, and therefore calculation becomes possible.
Using binary digits
A bit is a binary digit. It is the least unit of data in a computing device. The value of a bit is either 0 or 1 when storing informing or executing instructions. For example, decimal numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are represented in binary form in a computer, as shown below.
0=0, 1=1, 2=10, 3=11, 4=100, 5=101, 6=110, 7=111, 8=1000, 9=1001, 10=1010
Unlike the decimal/denary number system which applies the power of ten (10n), binary uses the power of two (2n) i.e.
Decimal system/ base 10
101 = 10
103 = 1,000
Binary system/ base 2
21 = 2
22 = 4
23 = 8
To clearly understand how to do math in a computer, it is essential to note that the calculation of binary starts from right to left. On the left is the most significant bit (MSB), and on the absolute right is the least significant bit (LSB). Starting with “1” from the right, an 8-bit number would be;
128 64 32 16 8 4 2 1
8-bits are equal to 1 byte. When adding in the binary counting system, the bit rules outlined below apply.
0+0=0, 1+0=1, 0+1=1, 1+1=0
Adding all the numbers above equals to 421.
42110 = 1101001012
Using Boolean logic
Computers operate using Boolean logic. That is a simple method to discover the “true” state of an expression in the binary numbering approach. Boolean operators AND, OR, XOR, and NOT evaluate values to give a true (1) or false (0) outcome. For intricate calculations, the computer processor interlinks several Boolean statements to produce accurate results.
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