Mathematics For Computer Science - Conversion of binary and hexadecimal numbers to decimal numbers

​Worked examples
a Convert the binary number 0101 to decimal.
Step 1: put the binary number into the table format as shown in Table

	1	Value	1
x base to the power 3	x base to the power 2	x base to the power 1	x base to the power 0

Step 2: binary is base 2, so replace the word ‘base’ with 2.

	1		1
x 2 to the power of 3	x 2 to the power of 2	x 2 to the power of 1	x 2 to the power 0

Step 3 calculate each column 

	1	Value	1
0 x 2 x2 x2 = 0	1 x2 x2 =4	0 x 2 =0	1x 1=1

​Step 4: add the columns together.
0 + 4 + 0 + 1 = 5

Convert the hexadecimal number 1D9 to decimal.
Step 1: put the hexadecimal number into the table format as shown in Table

1	D	9
x base to the power of 2	x base to the power of 1	x base to the power 0

​Step 2: hexadecimal is base 16, so replace the word ‘base’ with 16.

1	D	9
x 16 to the power of 2	x 16 to the power of 1	x16 to the power 0

​Step 3: calculate each column, replacing any letters with their numerical equivalent. (D = 13)

1	D	9
1x16x16 =256	13 x16=208	16x1=0

​Step 4: add the columns together.
256 + 208 + 9 = 473