There is a special relationship between binary and octal and binary an hexadecim

Question

There is a special relationship between binary and octal and binary an hexadecimal.

23 = 8 so to convert a number from binary to octal all that is necessary is to start at the right of the number, mark off 3 bits, convert those bits to decimal. The resulting number is the octal equivalent:

Take the binary number 111110110. Break it up into sections of 3 bits each:

111 110 110

Convert each section using the formula b * 22 + b * 21 + b* 20 and you get the octal number 766

Similarly, 24 = 16 so to convert a number from binary to hexadecimal all that is necessary is to start at the right of the number, mark off 4 bits, convert those bits to decimal. The resulting number is the hexadecimal equivalent.

Take the binary number 10101001. Break it up into sections of 4 bits each:

1010 1001

Convert each section using the formula b * 23 + b * 22 + b * 21 + b* 20 and you get the hexadecimal number A9

Convert the following binary numbers to octal:
1000001 =
10000010 =
1100010 =

Convert the following binary numbers to hexadecimal:
11100111 =
01101110 =
01111111 =

Explanation / Answer

binary=octal 1 000 001 = 101 10 000 010 = 202 1 100 010 = 142 binary = hexadecimal: 1110 0111 = E7 0110 1110 = 6E 0111 1111 =7F

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