Question

1. (a) (b) How many bits are required to represent the number -534 in 2's complement binary? Express the binary number. (b) Demonstrate the 2's complimentary subtraction of 13-6.

Answer 1

Detailed solution has been given below. However, if still any doubt or query, feel free to ask in the comments section, i'll be happy to help you out with that.

Tirupati Date: Page Sol). Part A Convert -534 inte binary: We Will wote binory_notation for_534. Do :- (534) - (9000010110), slow we see that binary notation Of (534) contains total of_10_bits. * Also, two comblement of any number must be either written in 4,8,16,32 bits depending upon the length. Sau here a minimumum of 10 bits are_tequired to represent 534, thus '8 hits are not enough for representation, and so the correct representation will be done in 16 bits as follows, by_butting additional zeroes: (534)10 (0000_0010 0001 0110) ट Ist complement of 534 will be written as → (1111 1101 1110 1001), Flipping os and is z's combliment 1111 1101 1110 1001 + 0000 0000 0000 0001 1111 1101 1110 1010 1 Adding to 1's compli} ment Thus_ (-534) = 2's compliment of_534 (111.1.1109_1110_1010),

201 Tirupati. Date: 1 Page: (b) demonstrałc_a's complimentary subtraction of 13-6 Herez__(13) _$1107 1011012 I's compliment [ 1001)2 10 of 6 2's combliment of 6 [ 10101 Now 2's compliment' of 6 =(-6,0 = [ 1010), .: (-6) [1010), © NOW. (13-6) can also be seen as addition of 13_and (-6) ie 13+ (-6) Puiting decimal_hotahons of 13 and -6 from equation a_and (D_,_add adding them together, we ad the decimal nolation of 13-6 = 13+(-0) (13-6), 1.0 + 1101 1010 0111 (13310 (-6) 1. (13-6)10 = (0111)2 = (7)901