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# CH1B - Introduction Number systems y and Conversion(B Hasan...

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Introduction, Number systems and Conversion (B) Hasan Zidan Department of Electrical Engineering AUST 1

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Binary Arithmetic The rules for binary ( + ) rithmetic are: The rules for binary ( - ) btraction are: arithmetic are: 0 + 0 = 0, carry = 0 subtraction are: 0 - 0 = 0, borrow = 0 1 + 0 = 1, carry = 0 rry 1 - 0 = 1, borrow = 0 orrow 0 + 1 = 1, carry = 0 1 + 1 = 0, carry = 1 0 - 1 = 1, borrow = 1 1 - 1 = 0, borrow = 0 Carries, Borrows to / from left of current digit. Binary addition , subtraction works the same as decimal addition, 2 subtraction .
Binary, Decimal Addition Decimal 1 0 1 0 1 1 Binary 1 1 3 4 + 1 7 -------- + 0 0 0 0 0 1 --------------- 5 1 From LSD to MSD: carry next 1 0 1 1 0 0 From LSB to MSB: = carry 7+4 = 1 ; carry 1 to next column 1 (carry) + 3 + 1 = 5. 1+1 0 , carry 1 1 (carry)+1+0 = 0 , carry 1 1 (carry)+0 + 0 = 1 , no carry answer = 5 1 . 1 +0 = 1 0 + 0 = 0 1 + 0 = 1 3 answer = 1 0 1 1 0 0 2

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Subtraction Decimal Binary 91 0 0 9 0 0 - 0 0 1 1 0 0 -0 0 1 10 1 ---------- 8 9 9 --------- 0 1 1 0-1 = 9 ; borrow 1 from next column 0 -1 (borrow)-0= 9 , 0-1 = 1 ; borrow 1 from next column orrow) () , borrow 1 9 - 1 (borrow) - 0 = 8 . nswer = 0 -1 (borrow) - 0 = 1 , borrow 1 1 - 1 (borrow) - 0 = 0. 4 Answer = 8 9 9 . Answer = 0 1 1 .
Binary Multiplication The rules for binary ( * ) rithmetic are: 0 * 0 = 0 arithmetic are: 1 1 0 1 ---------------- 1 1 0 1 * 1 0 1 1 (multiplicand) (multiplier) 1 * 0 = 0 1 1 0 1 0 0 0 0 1 1 0 1 0 * 1 = 0 * = ---------------- 1 0 0 0 1 1 1 1 2 = 143 10 ( Product ) 1 1 1 5

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Binary Division 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 (dividend) (divisor) (quotient) 1 0 1 1 1 1 1 0 011 () 1 0 1 1 1 1 0 1 1 0 1 1 artial remainder) 1 0 (partial remainder) 6
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CH1B - Introduction Number systems y and Conversion(B Hasan...

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