H.4. Converting from Binary, Octal or Hexadecimal to Decimal

We’re accustomed to working in decimal, and therefore it’s often convenient to convert a binary, octal, or hexadecimal number to decimal to get a sense of what the number is “really” worth. Our diagrams in Section H.1 express the positional values in decimal. To convert a number to decimal from another base, multiply the decimal equivalent of each digit by its positional value and sum these products. For example, the binary number 110101 is converted to decimal 53, as shown in Fig. H.8.

Fig. H.8. Converting a binary number to decimal.

Converting a binary number to decimal
Positional values:	32	16	8	4	2	1
Symbol values:	1	1	0	1	0	1
Products:	1*32=3	1*16=1	0*8=0	1*4=4	0*2=0	1*1=1
	2	6
Sum:	= 32 + 16 + 0 + 4 + 0s + 1 = 53