In base 7,a number is written only using thedigits0, 1, 2,6. The number 135 inbase 7 is 1 x 72 + 3 x 7 + 5 = 75 in base 10. What is the sum of the base 7 numbers 1234 and 6543 in base 7?
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(1234)₇≡ 1×7³+2×7²+3×7¹+4×7⁰
=343+49+21+4
=(466)₁₀
(6543)₇≡6×7³+5×7²+4×7¹+3×7⁰
=2058+245+28+3
=(2334)₁₀
2334+466=2800
7|2800|0
_____
7|400 |1
_____
7|57 |1
_____
7|8 |1
_____
1
∴, The sum is : (11110)₇
=343+49+21+4
=(466)₁₀
(6543)₇≡6×7³+5×7²+4×7¹+3×7⁰
=2058+245+28+3
=(2334)₁₀
2334+466=2800
7|2800|0
_____
7|400 |1
_____
7|57 |1
_____
7|8 |1
_____
1
∴, The sum is : (11110)₇
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