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. 2^3 = 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 * 2^2 + b * 2^1 + b* 2^0 and you get the octal number 766. Similarly, 2^4 = 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 * 2^3 + b * 2^2 + b * 2^1 + b* 2^0 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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