Question

Convert 16.5 (base 16) to decimal. Show the result with four digits after the decimal point. Show work.

Answer 1

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Convert 16.5 hexadecimal into decimal

To covert hexadecimal into decimal we will use following equation

If hexadecimal has digit (d₃d₂d₁d₀) than its equivalent decimal value is

Decimal= d₃*16³+ d₂*16²+ d₁*16¹+ d₀*16⁰   

for digit after .(dot) it is divided by power of 16 (similar like binary to decimal)

Hence over here 16.5 hexadecimal is given

Decimal=1*16¹+6*16⁰+5*16^-1

                =1*16+6*1+5/16

                =16+6+0.3125

                =22.3125

In another way we first convert hexadecimal into binary and then convert binary into decimal

Hexadecimal 16.5 into binary

16.5= 0001 0110. 0101 (each hexadecimal digit represented using 4 bit binary)                  

To convert hexadecimal number into binary use the following table

Hexa decimal	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A	1010
B	1011
C	1100
D	1101
E	1110
F	1111

Now convert this 0001 0110. 0101 into decimal

Decimal= 1*2⁴+0*2³+1*2²+1*2¹+0*2⁰+ 0*2^-1+1*2^-2+0*2^-3+1*2^-4

                =1*16+0*8+1*4+1*2+0*1+(0/2)+(1/2²)+(0/2³)+(1/2⁴)

                =16+0+4+2+0+0+(1/4)+0+(1/16)

=16+0+4+2+0+0+0.25+0+0.0625

                =22.3125