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NDA Math Binary Numbers
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© examsnet.com
Question : 3
Total: 13
A binary number is represented by
(
c
d
c
c
d
d
c
c
c
d
d
d
)
2
, where c > d. What is its decimal equivalent?
[NDA II 2019]
1848
2048
2842
2872
Validate
Solution:
Binary numbers are represented by 0’s and 1’s
Given, c > d
∴
(
c
d
c
c
d
d
c
c
c
d
d
d
)
2
=
(
101100111000
)
2
(
101100111000
)
2
=
(
1
×
2
11
)
+
(
0
×
2
10
)
+
(
1
×
2
9
)
+
(
1
×
2
8
)
+
(
0
×
2
7
)
+
(
0
×
2
6
)
+
(
1
×
2
5
)
+
(
1
×
2
4
)
+
(
1
×
2
3
)
+
(
0
×
2
2
)
+
(
0
×
2
1
)
+
(
0
×
2
0
)
=
2
11
+
2
9
+
2
8
+
2
5
+
2
4
+
2
3
=
2
3
+
2
4
+
2
5
+
2
5
(
2
3
+
2
4
+
2
6
)
=
8
+
16
+
32
+
32
(
8
+
16
+
64
)
=
56
+
32
(
88
)
=
56
+
2816
=
(
2872
)
∴
(
101100111000
)
2
=
(
2872
)
10
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