How to Convert Denary to Binary

Step by Step Guide for Year 7

What is Binary?

Firstly, binary is a numeric system which uses two numerals to represent all real numbers. While the most common counting system (the decimal system) uses ten numerals, binary uses 0 and 1. Usually we use base 10( the decimal system) the denary system but a computer uses base 2 and there are 2 different digits (1 and 0) and the first few numbers are 1,10,11,100,101,110,111,1000 and 1001. In Arithmetic, base 2 is actually easier than base 10 but the numbers are much longer.A denary number is a number in the base 10 or more commonly known as the decimal system. The base of a numeral system refers to the number of numerals that are used for expressing a number in that system. Denary numbers use 10 numerals these are 0,1,2,3,4,5,6,7,8, and 9.

Conversion & Adding Binary numbers

Converting Denary to Binary and Vice Versa

When converting denary to binary you have any number for example 145. Then we try to make that number using the rule of base 2 with each section doubled by the one before so, in this case we have 1,2,4,8,16,32,64 and 128. Then we see if our chosen number is greater or equal to numbers on base 2,put down 1 if its greater than or 0 if its smaller than. When we get the total of our number we should have our binary code in this case it is 10010001 which is an 8bit binary number. Converting binary back to denary is another story, you have the binary code with 1's and 0's and you place them under the base 2 numbers adding up the number if there is a 1 underneath but don't add the numbers with a 0 underneath.

Adding together 8bit binary numbers

Adding binary numbers is similar to adding binary number but you need to abide by the rule which is that 0+1=1 either way round, 1+1=10 putting down zero and carrying the 1 and 1+1+1=11 putting down 1 and carrying the other 1. You can look below for a 4bit version of adding binary numbers