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ABIBLO COMPUTER SCIENCE

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

9/2/2020

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​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
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