Question

For the following decimal numbers, convert to 8-bit binary numbers and perform addition. Use 2's complement signed numbers when subtraction is indicated. (a) 2710+ 3410 (b) 520-1810 (c) 3110 - 6310

Answer 1

© @ (21),0 + (34)70 Step 1: Connect both decimal numbers to its equinalent binary number 2121 2134 213.-1 (81). - (1101), 25-1 17-0 (34) =(100010), 1940 1 26-1 a 4-0 22-0 1 - 0 Step 2: Represent these binary number in 8 bits by adding zerds to its left to make it of 8 bit (27)10 = 00011 011 (34) = oolooolo Step 3: Perform binary addition of the 8 bit binary numbers 00011011 00100010 00111101 :. (21): +(34) = (00111101), © (52), -(18,0 deamal number to its equivalent binar binary Step 1: Convert both numbers 2152 2119 29-0 2 26-0 (52) = (1 10100), (18770+ (10010), T3-0 a 16-1 23-0 al 2-0 TI-O 1-1

Step 2: Represe . Represent these binary number in 8 bits ... 210 = (00110100), (18). - (00010010), Slenge* Use a's compler - find 2's complement of Ase 2's complement numbers when subtraction is given. Subto act using a's complement. follow the following steps a's complement of subhahend - Add minuend (Ist number) and a's complement of subtrahend I - If addition produces carry, discard carry. If addition a produces no carry, takes a complement of sum & assign negative - Step 3.0 So, let's take as complement of subtrahend which is 18. (18) -(00010010) First take one's complement of this number & then add 1 Leign pol PPDP 11100101 II10I 110 so, a's complement of (18) 10 is (11101110), Step 4: Add minuend which is (5210 to 2's compleraent of (18) - docard 00110100 1 110110 00100010 Thus, addition of slavero todom the numbers produced a carry, so discard the carry. The remaining bits is the sum

Thus, (52).. - (18),0 =(00100010), © (31)70 -(63)70 Steps: Connect both decimal number to binary numbers 2/31 2163 215-1 (31) = 0.1)) 231-! (63), 0 = (1 111), 2 15-1 2 TL 217-1 213 23-1 11-1 Step 2: Represent the binary number in 8 bits. (31), -(0001 ), (63) = (001111), Step 3: To pefform 2's complement subtraction, take a's compte complement of subtrahend, that is, (63), (63)10 = (bunu), 11 000 000 11000001 So, 2's complement of (63) is (11000001). Step 4: Add minuhend (31), to a's complement of (63) 10 OOOLLLLL 11 000001 TI 100 000 Here, the sum of the number's doesn't produce carry.

thou of the rence, carry is no carry take & 2's complement sum and assign negative sign. So, take as complement of (1110000012 OOOIT - 00000000 Hence, (31), -(63),6 = -(00100000),