# 1. Convert 11110101 into decimal (2 marks). Show your working.?

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• Anónimo
hace 1 mes

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• Anónimo
hace 1 mes

Assuming it's trinary, 6561 - 27 - 3 = 6531

• Assuming that this is a base 2 number

....1 ....  1 ...... 1 ..... 1  0  1  0  1

= 2^7 + 2^6 + 2^5 + 2^4+ 0*2^3+ 2^2+ 0*2^1 + 2^0

= 128 + 64 + 32 + 16 + 0 + 4 + 0 + 1

= 245

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• Hi,

A simple way to do it is just to write the powers of 2 and add the results.

It’s easier to start from the right.

1*2^0 +0*2^1+1*2^2 +1*2^3 +0*2^4 +1*2^5 +1*2^6 +2*2^7

If you’re just looking for an answer, rather than all the math, you just do the

Following:

128+64 +32+16 +0 +4 +0 +1

Then add them. That equals 245

This answer is correct. I checked on a program I wrote for my TI-84 Calculator.

formeng

• 11110101(binary) = 128 + 64 + 32 + 16 + 4 + 1 = 245(decimal)

• 1 x 2^7 = 128

1 x 2^6 = 64

1 x 2^5 = 32

1 x 2^4 = 16

0 x 2^3 = 0

1 x 2^2 = 4

0 x 2^1 = 0

1 x 2^0 = 1

...........----------

• Looks like binary to me.  The simplest way to convert binary to decimal is to start with a decimal result of zero, then for each bit of the binary number from left to right simply double the previous result and add the bit value (zero or one) to get a new result.

1 + 2*0 = 1

1 + 2*1 = 3

1 + 2*3 = 7

1 + 2*7 = 15

0 + 2*15 = 30

1 + 2*30 = 61

0 + 2*61 = 122

1 + 2*122 = 245

There are fewer steps if you know all the powers of 2 involved in decimal.  Those are the place values in a binary number, from right to left: (1, 2, 4, 8, 16, ...).  So:

11110101₂ = 1 + 4 + 16 + 32 + 64 + 128 = 245

• For all we know, it may be in decimal already. What is the base?

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