Answer to Question #32237 in Math for hoa

Question

convert these 5 to each of the ff denary octal hexadecimal with formula 1.10100101 2.1110111 3.1010101 4.111111111 5.1001001

Answer 1

1.Converting from octal to binary is as easy as converting from binary to octal.
Simply look up each octal digit to obtain the equivalent group of three binary
digits.
Binary to Hexadecimal:
If the binary number is 10100101 then in order to convert it in
Hexadecimal in shortcut method you need to broke this number by taking four
digits at a time.
So, if we do that. it will be. 1010 & 0101
And now convert 1010 to Hexadecimal & answer will be A in
Hexadecimal & conversion of 0101will be 5

So, Binary 10100101 in Hexadecimal will be A5.

To convert binary to octal, split it every 3 digits then take the value of
those groups
10100101 = 010 100 101 = 245 octal
2. Binary to Hexadecimal:
If the binary number is 1110111 then in order to convert it in
Hexadecimal in shortcut method you need to broke this number by taking four
digits at a time.
So, if we do that. it will be. 0111 & 0111
And now convert 0111 to Hexadecimal & answer will be 7 in
Hexadecimal & conversion of 0111 will be 7

So, Binary 1110111 in Hexadecimal will be 77.
To convert binary to octal, split it every 3 digits then take the value of
those groups
1110111 = 001 110 111 = 167 octal

3. Binary to Hexadecimal:
If the binary number is 1010101 then in order to convert it in
Hexadecimal in shortcut method you need to broke this number by taking four
digits at a time.
So, if we do that. it will be. 0101 & 0101
And now convert 0101 to Hexadecimal & answer will be 5 in
Hexadecimal & conversion of 0101will be 5

So, Binary 1010101 in Hexadecimal will be 55.

To convert binary to octal, split it every 3 digits then take the value of
those groups
1010101 = 001 010 101 = 125 octal
4. Binary to Hexadecimal:
If the binary number is 111111111 then in order to convert it in
Hexadecimal in shortcut method you need to broke this number by taking four
digits at a time.
So, if we do that. it will be. 0001 1111& 1111
And now convert 0001 to Hexadecimal & answer will be 1 in
Hexadecimal & conversion of & 1111 will be F

So, Binary 111111111 in Hexadecimal will be 1FF.

To convert binary to octal, split it every 3 digits then take the value of
those groups
111111111 = 111 111 111 = 777 octal
5.Binary to Hexadecimal:
If the binary number is 1001001 then in order to convert it in
Hexadecimal in shortcut method you need to broke this number by taking four
digits at a time.
So, if we do that. it will be. 0100 & 1001
And now convert 0100 to Hexadecimal & answer will be 4 in
Hexadecimal & conversion of & 1001 will be 9

So, Binary 1001001 in Hexadecimal will be 49.

To convert binary to octal, split it every 3 digits then take the value of
those groups
1001001 = 001 001 001 = 111 octal