Binary Integers

        

Calculating denary integers represented by a binary integer

• Denary integers are worked out by using the unit 10.

Binary Integers

• In the same way binary integers can be worked out as numbers based on the number 2.
• Therefore 10010100 represents the denary number 148 and we can write the answer in the table:

• 10010100 Binary  =  1x128+0x64+0x32+0x8+1x4+0x2+0x1 Denary

         = 128 + 16+4 (denary)

         = 148 (denary)

So if you want to convert a binary integer into its denary equivalent, just write it in a table like this and add up the values in the columns which have a bit value of 1.  

Convert binary integers to denary

Work out which denary integers are represented by these Binary Integers.

 

1. 00111010 =

• 00111010 Binary  =  1x32+1x16+1x8+1x2=

         = 32+16+8+2

         = 58

2. 11101111 =

• 11101111 Binary  =  1x128+1x64+1x32+1x8+1x4+1x2+1x1

         = 128+64+32+8+4+2+1

         = 239

3. 01000011 =

• 01000011 Binary  =  1x64+1x2+1x1

         = 64+2+1

         =

4. 10010100 =

• 10010100 Binary  =  1x128+1x16+1x4

         = 128+16+4

         = 148

5. 00000000 =

• 00000000 Binary  =  0

          = 0

          = 0

6. 11111111 =

• 11111111 Binary  =  1x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1

        = 128+64+32+16+8+4+2+1

        = 255

Calculating which binary integer represents a denary integer

• To convert a denary integer to their binary integer equivalents, you simply work in reverse.

Denary integer

• Start on your left.
• Check whether the denary number 205 is greater that the number in the first column 128.
• In this case it is which means that we need 128 in the number, so place 1 in the column.
• 205 – 128 = 77
• 77-64 = 13
• Moving to the next column, check whether 13 is greater that the number in the next column 32.
• As it is not, we place 0 in the column.