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Published byElijah Walsh Modified over 10 years ago
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Binary Addition Rules Adding Binary Numbers 0 + 1 = 1 1 + 0 = 1
0 + 0 = 0 1 + 1 = 0 (carry one) carry = 1 (carry one)
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Example 111111 1011011 +100111 --------------10000010 carries result
*** The last carry is placed at the left hand side
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Let’s try this… 101000 110100 111100 111101
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Let’s try this… 101011 110100 101111
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Subtracting Binary Numbers
Binary Subtraction Rules take the second value (the number to be subtracted) and apply TWO'S COMPLEMENT (change 1 for 0 and 0 for 1) add 1 to the result (of two’s complement) add the complemented value to the first value; during addition we disregard the last carry
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Example
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Let’s try this… – 111 110111 110010 11010
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Let’s try this… – 101 101001 11011
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Multiplying Binary Numbers
Binary multiplication can be achieved in a similar fashion to multiplying decimal values. Multiply each digit using the standard method; Add the results using the binary addition rules
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Example 1011 x 111 Notice the pattern in the partial products, as you can see multiplying a binary value by two can be achieved by shifting the bits to the left and adding zeroes to the right.
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Let’s try this… 11001 x 11 10011 x 101 x 110 11111 x 101 x 100
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Seatwork: x 111 x 1011 1000 11110
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Dividing Binary Numbers
Binary division can be achieved in a similar fashion to dividing decimal values. Divide the divisor from the dividend Use the simple subtraction rules whenever necessary, as follows: 0 – 0 = 0 1 – 1 = 0 1 – 0 = 1 0 – 1 = 1 (with borrow)
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Example 11 r = 10 11 )1011 -11 101 -11 10 <-- remainder, R
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Let’s try this… 100 / 10 111 / 11 1010 / 100 1101 / 11 10111 / 10 10 10 r 1 10 r 10 100 r 1 1011 r 1
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Compute the ff.: x 101 x 11 / 111 / 1010
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Compute the ff.: 1010 r 11 r 100
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