Question

1. 2. Find the decimal value of the following 8-bit numbers for (i) un-signed and (ii) signed number. (a) 11010110, (b) 01011101 Express the following decimal numbers in 6-bit 2's complement representation: (a) -27, (b) 6, (c)-13, (d) -47 - 4. Convert decimal numbers 83 and 101 to 8-bit unsigned binary number. Find the sum and difference (with addition approach) of these two numbers.

Answer 1

ig, is unsigned number decimal foom. 1091101011 0 - 1 1 0 1 0 1 , add their decimal values * (** 1) + (x1) + (ko) +(4x1) + Calo) +6% 1 2 +Caxv) 4x1) -a77a "tant op te =128764+16+4+2 = 214 (62 0 10111010101 110 ! y de 27 2o go ay as of a go . (@}0) +64) 463x0) +(2447) +x1) 4 (x 1) +Gex o) 4G021 = 64 +16 +8+4+1=93 multiply their decinal values with given digit nors and add then ii, Signed number decimal form. (a) 110101103 sign bit so, here if sign bit is 1; it in number

11010110 > Negative nori eigen bok s. Now = 1 101 0110 decimal value 24 [Ca 1) + 420) +(2417 +62x0) +f*(1) @x1) +a%o] -1 [64+0+16+0+4+2+0] +86 -86 signed bit Day 01011101 oloi 1101 signed bit 'o so it is a poritive number . Now :o 101 1101 decimal value. 2016.07 +65x0) +Gx1)-63x07768x17 ? 48'2014G*19] 20 | 64+0+16+8+4+0+1] 50 93 9+93 signedbit positive number

33 0)-27 13- (6-1 a 3-0 1-1 27,03 110110 Here we got 5-bit value of at in binary now to get a bit value extend it with aigned number - 11011 abbit value. eignedbit NOW 11 1012 1th complement no 0100 90 0101 100101.2 ik ok complement of 2007. (6) 6. 6,0211023-1 Here we got 8-bit value of Lolo into banorg format . Now extend it with signed number . 000110 extended values of bit as it is politive nor.

for a positive binaryl decimal representation it's die complement in diginal binary form 6,0 = 000110, 38's complement : to @ é -13. . 24 2112 2137 & Z 13 - 1101 als As it is negative number sien extention 1-1 to be done with as. I11101 sign extension Now I 11101 - complement TO0010 add to 100011 1 oooll is as complement representation of 1310)

ed) -47 of of 183-1 a (11-1 47 decinal=1011 19 binery (0) 0 y gel As it is negative incomber and 6-bit volue: no need of sign extension, do is complement of dart sbits. = 1 10000 ... adda HII Trooo! -110001, in a's complement of 47.

) 836 >binary value = 1010016, 2010-) birong value • 110010101 converting them into 8-bit unsigned value 8310 101001lay 0101 0011(c) 101,0 11001018) 0110 010162) Adding of a uneigned notre. 83 0101 0011 101 - 0110 0101 ansatoil iddo anks 1011 1000 a converting to decimal = @x0) + (O KO) +(881 -6 14 1) - 8x22 + xo) to'xo) +6220) = 188 +32 + 16 + 8 = 184

Serb traction of two unsigned numbeo's, Two complement of 10 0110 0101 gi compleanet of 10110 : 1001 1010 add +1 1001 1010 1001 1011 Now 83. - 101 = -18. 10 10 01010011 Tool lol Trio Trio Lao an complement of it 110 1110 eignbit at answer is negative number 1.110 1110 ths complement Fool cool add +1 1 1001 0010 Signbit .: 886-1010 = -18,0 = 1001 0016.. rol signbit