This document provides information on converting between denary and binary number systems. It gives an example of 217 in denary format and 11011001 in binary format. It then asks what denary number 11011001 represents in binary. It provides two methods for converting: 1) using binary columns and adding up the place values for 1s and 2) using binary columns and subtracting the largest value from the number until reaching 0. It concludes by showing 202 converted to binary as 11001010 using the subtraction method.

1. Convert Denary to Binary (and back again)
Denary: This isthe base 10 system,thismeansthatwe use 10 symbolstorepresentthe numbers(0,1,2, 3, 4, 5,
6, 7, 8, 9) and we use units,tensand hundreds,the number217 can be shownas:
100 10 1
2 1 7
Binary: This isthe base 2 system;there are only2 symbols(0and1):
128 64 32 16 8 4 2 1
1 1 0 1 1 0 0 1
Question: What denary number is shown above in binary (11011001)?
For the GCSE Computing course you need tobe able to:
“Convert positive denary numbers 0 – 255 into 8 bit binary numbers and vice versa”
There are 2 easy methods to convertdenary (base 10 ) to binary (base 2):
Convertbinary (base 2) to denary (base 10):
Put the binarynumberintothe columnsandadd upthe value of the columnswith1 inthem:
128 64 32 16 8 4 2 1
1 1 0 0 1 0 1 0
Gives: 128 + 64 +8 +2
Answer: 202
Use binary columns and take it away
Convertdenary 202 into binary:
202 74 10 2
128 64 32 16 8 4 2 1
1 1 0 0 1 0 1 0
Searchfor the largestbinarycolumnheadingwe
can subtract fromthe number,take itawayand
repeatwiththe remainderuntil we getananswer
of 0
Answer: 11001010