Question 21Express the following binary numbers into their equivalent octal numbers:(a) 100101111(b) 111011010(c) 1010011(d) 10011101

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Accepted Answer

(a) 100101111Grouping in bits of 3:100undefined101undefined111undefined\underlinesegment{100} \quad \underlinesegment{101} \quad \underlinesegment{111}100​101​111​BinaryNumberEquivalentOctal100410151117Therefore, (100101111)2 = (457)8(b) 111011010Grouping in bits of 3:111undefined011undefined010undefined\underlinesegment{111} \quad \underlinesegment{011} \quad \underlinesegment{010}111​011​010​BinaryNumberEquivalentOctal111701130102Therefore, (111011010)2 = (732)8(c) 1010011Grouping in bits of 3:001undefined010undefined011undefined\underlinesegment{001} \quad \underlinesegment{010} \quad \underlinesegment{011}001​010​011​BinaryNumberEquivalentOctal001101020113Therefore, (1010011)2 = (123)8(d) 10011101Grouping in bits of 3:010undefined011undefined101undefined\underlinesegment{010} \quad \underlinesegment{011} \quad \underlinesegment{101}010​011​101​BinaryNumberEquivalentOctal010201131015Therefore, (10011101)2 = (235)8

Binary Number	Equivalent Octal
100	4
101	5
111	7

Binary Number	Equivalent Octal
111	7
011	3
010	2

Binary Number	Equivalent Octal
001	1
010	2
011	3

Binary Number	Equivalent Octal
010	2
011	3
101	5

Data Representation and Boolean Logic — Question 21

Question 21