1 Take your binary number calculated in question 1 and conve

1. Take your binary number calculated in question 1 and convert it, using the INSPECTION method, to: a) octal b) hexadecimal c) base 4 Check each answer by converting it back to decimal and compare with the last four digits of your student number.

Binary Number: 11111111010

student number: 1502042

Please show working outs

Solution

1) Binary to Octal using Inspection method

011 111 111 010

Here divide them into group of three bits each and assign them 4 21 starting from left to right as follows:

4 2 1 4 2 1 4 2 1 4 2 1

0 1 1 1 1 1 1 1 1 0 1 0

Now multiply the bit with nunber assigned to it and add output of all the bits in one group

4*0+2*1+1*1 4*1+2*1+1*1 4*1+2*1+1*1 4*0+2*1+1*0

0+2+1 4+2+1 4+2+1 0+2+0

3 7 7 2

Hence octal conversion is 37728

Now when converting binary to hexadecimal we will see 16 which is power is 2, that is four hence we will divide the bits into group of four and assign each bit 8 4 2 1 starting from left to right.

0111 1111 1010

8 4 2 1 8 4 2 1 8 4 2 1

0 1 1 1 1 1 1 1 1 0 1 0

Now again multiply each bit in group by number above it and add these numbers with group

8*0+4*1+2*1+1*1 8*1+4*1+2*1+1*1 8*1+4*0+2*1+0*1

0+4+2+1 8+4+2+1 8+0+2+0

7 15 10

7 F A

Hence binary to hexa is 7FA₁₆