Сложить числа. Проверять правильность вычислений переводом исходных данных и результатов в десятичную систему счисления.
а) 1101100000(2) + 10110110(2); б) 101110111(2) + 1000100001(2); в) 1001000111,01(2) +
+ 100001101,101(2); г) 271,34(8) + 1566,2(8); д) 65,2(16) + 3CA,8(16).
Решение
А) 1101100000(2) + 10110110(2) = 10000010110(2)
1101100000(2) = 0∙20+0∙21+0∙22+0∙23+0∙24+1∙25+1∙26 +0∙27+1∙28+1∙29 = 864(10)
10110110(2) = 0∙20+1∙21+1∙22+0∙23+1∙24+1∙25+0∙26 +1∙27 = 182(10)
10000010110(2) = 0∙20+1∙21+1∙22+0∙23+1∙24+0∙25+0∙26+0∙27+0∙28+0∙29+1∙210 = 1046(10) = =864(10)+182(10)
б) 101110111(2) + 1000100001(2) = 1110011000(2)
101110111(2) = 1∙20+1∙21+1∙22+0∙23+1∙24+1∙25+1∙26 +0∙27+1∙28 = 375(10)
1000100001 (2) = 1∙20+0∙21+0∙22+0∙23+0∙24+1∙25+0∙26 +0∙27 +0∙28+1∙29 = 545(10)
1110011000(2) = 0∙20+0∙21+0∙22+1∙23+1∙24+0∙25+0∙26 +1∙27 +1∙28+1∙29 = 920(10) =375(10)+545(10)
в) 1001000111,01(2) + 100001101,101(2) = 1101010100,111(2)
1001000111,01(2) = 1∙20+1∙21+1∙22+0∙23+0∙24+0∙25+1∙26+0∙27+0∙28+1∙29+1∙2-2 = 583,25(10)
100001101,101(2) = 1∙20+0∙21+1∙22+1∙23+0∙24+0∙25+0∙26+0∙27+1∙28+1∙2-1+1∙2-3 = 269,625(10)
1101010100,111(2) = 0∙20+0∙21+1∙22+0∙23+1∙24+0∙25+1∙26+0∙27+1∙28+1∙29+1∙2-1+1∙2-2+1∙2-3 = =852,875(10) = 583,25(10) + 269,625(10)
г) 271,34(8) + 1566,2(8) = 2057,54(8)
271,34(8) = 1∙80+7∙81+2∙82+3∙8-1 +4∙8-2 = 185,4375(10)
1566,2(8) = 6∙80+6∙81+5∙82+1∙83+2∙8-1 = 886,25(10)
2057,54(8) = 7∙80+5∙81+0∙82+2∙83+5∙8-1 +4∙8-1 = 1071,6875(10) = 185,4375(10) + 886,25(10)
д) 65,2(16) + 3CA,8(16) = 42F,A(16)
65,2(16) = 5∙160+6∙161+2∙16-1 = 101,125(10)
3CA,8(16) = 10∙160+12∙161+3∙162+8∙16-1 = 970,5(10)
42F,A(16) = 15∙160+2∙161+4∙162+10∙16-1 = 1071,625(10)