Page 14 - TechPluse_C7_Flipbook
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Example 3: Convert (110011) to decimal.
2
1
0
2
5
3
4
= 1 × 2 + 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 1 × 2
= 32 + 16 + 0 + 0 + 2 + 1
= 51
(110011) = (51)
2 10
Example 4: Convert (100101) to decimal.
2
3
2
5
0
1
4
= 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 0 × 2 + 1 × 2
= 32 + 0 + 0 + 4 + 0 + 1
= 37
(100101) = (37)
2 10
Example 5: Convert (111100) to decimal.
2
4
5
1
0
2
3
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 0 × 2
= 32 + 16 + 8 + 4 + 0 + 0
= 60
(111100) = (60)
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Example 6: Convert (111111) to decimal.
2
1
3
0
2
5
4
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2
= 32 + 16 + 8 + 4 + 2 + 1
= 63
(111111) = (63)
2 10
Example 7: Convert (1000001) to decimal.
2
6
3
5
0
1
2
4
= 1 × 2 + 0 × 2 + 0 × 2 + 0 × 2 + 0 × 2 + 0 × 2 + 1 × 2
= 64 + 0 + 0 + 0 + 0 + 0 + 1
= 65
(1000001) = (65)
2 10
BINARY ADDITION
Binary addition is similar to the addition of decimal numbers. When the value of addition exceeds
the value 1, say 10 or 11, then 1 is carried over to the left of the current position. The rules for
adding two binary digits are given below:
X Y X + Y
0 0 0 + 0 = 0
0 1 0 + 1 = 1
1 0 1 + 0 = 1
1 1 1 + 1 = 10 (carry 1)
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