To find the sum of the binary numbers 1111, 1000, and 0100, we first align them for addition:
1111
+ 1000
+ 0100
-------
Adding column by column from the right, we get:
So, the final sum is 1 (carry) + 1 + 1 = 11, which in binary is 10111. Thus, the sum of 1111, 1000, and 0100 in binary is 10111.
To convert decimal numbers to Binary-Coded Decimal (BCD), each digit is represented by its 4-bit binary equivalent. For instance, 74 in BCD is 0111 0100, 38 is 0011 1000, 8884 is 1000 1000 1000 0100, 275 is 0010 0111 0101, 165 is 0001 0110 0101, and 9201 is 1001 0010 0000 0001. To add an odd parity bit, count the number of 1s in the BCD representation; if it's even, add a 1, and if it's odd, add a 0. For example, 74 becomes 0111 0100 1 (5 ones), and 38 becomes 0011 1000 1 (5 ones).
-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
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 0100 0046 ------ 1146 ------
1000
1000
Find the powers of 2. 8 in binary would be 1000