Converting Between Binary & Denary

Converting Denary to Binary Walkthrough:

• Write down the powers of 2 in binary from right to left, starting with 2⁰ (1), 2¹ (2), 2² (4), 2³ (8), and so on, until you reach 128 (as answers must be given in 8 bits)

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

• Starting from the leftmost column, write a 1 if the corresponding power of 2 is less than or equal to the number you’re converting, 171 in this example, otherwise write a 0.

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

• Check your working by adding together all column headings with a 1 underneath (128+32+8+2+1=171)
• Read the binary digits from left to right to get the binary equivalent of 171.
  10101011

Converting Binary to Denary Walkthrough:

• Write down the powers of 2 in decimal from right to left, starting with 2⁰ (1), 2¹ (2), 2² (4), 2³ (8), and so on, until you reach 128 (as answers must be given in 8 bits)

128

64

32

16

8

4

2

1

• Starting from the leftmost column, write the binary digit in the column if it is a 1 write 1, and write 0 if it is a 0.

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

• Add up the values in each column where the binary digit is 1.
  64 + 32 + 4 + 2 = 102