Converting Between Decimal & Binary (AQA GCSE Computer Science)

Decimal to binary conversion

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

Example 1

• To convert the decimal number 45 to binary, start by writing out the binary headings from right to left

128	64	32	16	8	4	2	1

• Start at the leftmost empty column heading (128). Is the decimal number > column heading? (45 > 128) No, put a 0 in the 128 column. Repeat until you put a 1 under a heading. In this example it would be 32
  

128	64	32	16	8	4	2	1
0	0	1

• Next subtract column heading from decimal value, 45-32 = 13
• Repeat previous two steps until you have a value under each column heading

128	64	32	16	8	4	2	1
0	0	1	0	1	1	0	1

• 32 + 8 + 4 + 1 = 45
• Decimal 45 is 00101101 in Binary

Example 2

• To convert the decimal number 213 to binary, start by writing out the binary headings from right to left

128	64	32	16	8	4	2	1

• Start at the leftmost empty column heading (128). Is decimal number > column heading? (213 > 128) Yes, put a 1 under the heading.
  

128	64	32	16	8	4	2	1
1

• Next subtract column heading from decimal value, 213-128 = 85
• Repeat process until you have a value under each column heading

128	64	32	16	8	4	2	1
1	1	0	1	0	1	0	1

• 128 + 64 + 16 + 4 + 1 = 213
• Decimal 213 is 11010101 in Binary

Example 1

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

8	4	2	1

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

8	4	2	1
1	0	1	1

• Add together any value with a 1 under it
• (1 x 8) + (1 x 2) + (1 x 1) = 11
• Binary 1011 is 11 in Decimal 

Example 2

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

128	64	32	16	8	4	2	1

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

128	64	32	16	8	4	2	1
0	1	1	0	0	0	1	1

• Add together any value with a 1 under it
• (1 x 64) + (1 x 32) + (1 x 2) + (1 x 1) = 99
• Binary 01100011 is 99 in Decimal