Converting Between Binary & Denary (Cambridge (CIE) O Level Computer Science)

Denary to Binary Conversion

How do you convert denary to binary?

• It is important to know the process of converting from denary to binary to understand how computers interpret and process data

• To convert from denary to binary you must start by writing out a binary number line

• Find the first column heading with a value larger than the denary value you are converting

• Write down each column heading to the right (not including the largest heading) until you reach 1

Example 1

• To convert the denary number 45 to binary, start by writing out the binary number line

• The first column heading larger than 45 is 64, so the number line would be:

• Start at the leftmost empty column heading (32)

• Divide column heading into denary number (how many times does 32 fit into 45?)

  • 1 time with 13 remaining

• Repeat with next column heading (how many times does 16 fit into 13?)

  • 0 times with 13 remaining

• Repeat until all columns have a binary value

• Denary 45 is 101101 in binary (6 bits)

Example 2

• To convert the denary number 3059 to binary, start by writing out the binary number line

• The first column heading larger than 3059 is 4096, so the number line would be:

• Start at the leftmost empty column heading (2048)

• Divide column heading into denary number (how many times does 2048 fit into 3059?)

  • 1 time with 1011 remaining

• Repeat with next column heading (how many times does 1024 fit into 1011?)

  • 0 times with 1011 remaining

• Repeat until all columns have a binary value

• Denary 3059 is 101111110011 in binary (12 bits)

Binary to Denary Conversion

• To convert from binary to denary, count how many bits make up the value

• Write out the column headings for the number of bits given from right to left

• Add together any column heading with a value of 1 in the column

Example 1 (4 bits)

• To convert the binary number 1011 to denary, start by writing out the binary headings from right to left

• Write in the binary digits under the headings from left to right

• Add together any column heading with a 1 under it

• (1 x 8) + (1 x 2) + (1 x 1) = 11

• Binary 1011 is 11 in denary 

Example 2 (8 bits)

• To convert the binary number 01100011 to denary, start by writing out the binary headings from right to left

• Write in the binary digits under the headings from left to right

• Add together any column heading with a 1 under it

• (1 x 64) + (1 x 32) + (1 x 2) + (1 x 1) = 99

• Binary 01100011 is 99 in denary 

Example 3 (14 bits)

• To convert the binary number 01110001110100 to denary, start by writing out the binary headings from right to left

• Add together any column heading with a 1 under it

• (1 x 4096) + (1 x 2048) + (1 x 1024) + (1 x 64) + (1 x 32) + (1 x 16) + (1 x 4) = 7284

• Binary 01110001110100 is 7284 in denary