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-123 = 11 1000 0101 [I presume the number 123 is in decimal] First write the positive number in binary using 10 bits (I've split it into groups of 4 bits to make it easier to read): 123 = 00 0111 1011 Convert to 1s complement by inverting all bits (any 0 => 1, any 1 => 0): 00 0111 1011 => 11 1000 0100 Finally add 1 to get 2s complement: 11 1000 0100 + 1 = 11 1000 0101 Thus the 2s complement of the negative number: -123 = 11 1000 0101 This can also be expressed in hexadecimal: -123 = 0x385 Or in octal (easy to convert if the binary number is first written in groups of 3 bits): -123 = 1 110 000 101 = 01605 [I've used C notation for the hexadecimal and octal numbers.]
0000 0000 1111 1000F ( or 15) = 1111 in binary, and 8 = 1000 in binary, so F is 1111 1000
1000
Find the powers of 2. 8 in binary would be 1000
Because computers are binary - meaning they represent all numbers using only two digits - the closest they can get to expressing 1000 in a nice rounded number is 1024 which is 2 raised to the 10th power (2^10). Written in binary, this number is 10000000000. Of course computers can represent the base 10 number 1000 but it's not as nice and neat. In binary, the base 10 number 1000 is written 1111101000.
1111 + 0001 + 1000 + 0100 = 11100 Remember that in binary, 1 + 1 = 10 (0 carry 1) and 1 + 1 + 1 = 11 (1 carry 1).
1. represent every individual digit of given hexadecimal in binary form like this 4---------> 0100 8---------> 1000 7---------> 0111 2. combine the individual binary digits in order to get the binary of given hexadecimal number 487 ------------> 0100 1000 0111 ( required binary number )
Write each hexadecimal digit straight into binary: 5 = 0101 4 = 0100 2 = 0010 So 0x542 = 0101 0100 0010 = 10101000010 (without the spaces). Hex digit to binary conversion: 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
Quick reference chart for converting Hexidecimal to Binary numbers: Hex 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
-123 = 11 1000 0101 [I presume the number 123 is in decimal] First write the positive number in binary using 10 bits (I've split it into groups of 4 bits to make it easier to read): 123 = 00 0111 1011 Convert to 1s complement by inverting all bits (any 0 => 1, any 1 => 0): 00 0111 1011 => 11 1000 0100 Finally add 1 to get 2s complement: 11 1000 0100 + 1 = 11 1000 0101 Thus the 2s complement of the negative number: -123 = 11 1000 0101 This can also be expressed in hexadecimal: -123 = 0x385 Or in octal (easy to convert if the binary number is first written in groups of 3 bits): -123 = 1 110 000 101 = 01605 [I've used C notation for the hexadecimal and octal numbers.]
0000 0000 1111 1000F ( or 15) = 1111 in binary, and 8 = 1000 in binary, so F is 1111 1000
8 in decimal is 1000 in binary
1000 = 8
1000
1000
Find the powers of 2. 8 in binary would be 1000
Yes, 888+88+8+8+8=1000