ECE15A-Homework1-Winter2014 (1)

A10100111b01100111are

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Unformatted text preview: epresent negative numbers, what range of integers can be stored in the computer? Express you answer in decimal. [ 26 1 1 1 ­ ­ ] ­ 1 ­ ­ , 26 1 1 [ 25 1 1 ­ ] ­ 1 ­ , 25 1 [377,377 ­26 26] 4. A computer has a word length of 8 bits including sign. A= 10100111, B = 01100111 are 2’s complement numbers. Perform the following operations and indicate whether overflow occurs: (2p) (a) A+B cry ar: 11x1x 1x11 A 0011(8) 1101 ­9 + B 1011(0) 0101 13 = 10010(goenwls i) 0011 inr e atbt ⇒ 0010(4 0011 1) N vrlw(attocrybt r ae o+e a ee ooefo ls w ar isaesm,psngcnnvr oefo) vrlw (2p) (b) A­B ­ B= 1010+ 0101 01001=1010 cry ar: 1111x 0111 A 0011(8) 1101 ­9 +­) (B 0101(13 1010 ­0) = 11000(12 1000=(4 0000 ­9)⇒ 0000 6) Oefo a curd(attocrybt r ifrn,ngngps vrlwhsocre ls w ar isaedfeet e+e=o i hscs hc sbd nti aewihi a) (2p) Give the decimal values of A and B A : 1101 0011 = ­0010+) (11001 = ­1101 0010 = ­6+681 (41++) = ­9 8 B : 0101 1011 = 6+2421 43+++ = 13 0 5. A computer has a word length of 8 bits including sign. Convert decimal +67 and +18 to binary using the signed 2’s complement representation. Then perform the binary equivalent of : Convert the answers back to decimal and verify that they are correct. (6) +7: 6/ =3+ 72 31 3/ =1+ 32 61 1/ =80 62 + 82 =40 / + 42 =20 / + 22 =10 / + 12 =01 / + 1 0 0 1 ⇒ 1 0 0 1 ( 6 ) 001 0001 +7 (6) ­7: 0001 1001 1110+ 01101 1110(6) 0111­7 (1) +8: 1/ =90 82 + 92 =41 / + 42 =20 / + 22 =10 / + 12 =01 / + 1 0 0 ⇒ 0 1 0 0 ( 1 ) 01 0001...
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