Addition and Substraction Binary 3 Addition and Substraction

Binary Addition Binary addition follows the same rules as decimal addition Put the two numbers you want to add one above the other Add them up column by column, and bring any carry’s to the following column (Once you have calculated your result – check your result again the decimal result)

Binary Addition 01101 + 01110 ------------- NOTE: 0 + 0 = 0 0 + 1 = 1 1 + 1 = 0 + carry of 1 1 + 1 + 1 = 1 + carry of 1 01101 + 01110 ------------- Convert each number to decimal and see if your calculation was correct

Binary Addition Complete the following additions 01001 01100 + 01111 ------------- 01100 + 01110 ------------- 0100011 + 0110110 ------------------ 10101101 + 11010110 -------------------

Binary Addition Complete the following additions 01001 01100 + 01111 ------------- 11000 01100 + 01110 ------------- 11010 0100011 + 0110110 ------------------ 1011001 10101101 + 11010110 ------------------- 110000011

Binary Subtraction To subtract, Convert the positive numbers take a two’s complement of any negative numbers take a two’s complement of any number to be subtracted Add the two numbers and interpret the result If the left most bit is a 1, the number is negative and we take a two’s complement to determine what negative number it is

Binary Subtraction 5  0000 0101 3  0000 0011 1111 1101 Add together: 0000 0101 1111 1101 --------------- 1) 0000 0010 Ignore the carry, and the result is positive 2

Binary Subtraction 3  0000 0011 5  0000 0101 1111 1011 Add together: 0000 0011 1111 1011 --------------- 1111 1110 The left most bit indicates its negative, take a two’s 0000 0010 answer is -2

Binary addition & subtraction Complete the following exercises (convert to two’s complement binary representation before completing the addition. Interpret your two’s complement result) 6 + 4 10 + 12 11 – 5 18 – 22 8 – 3 -3 – 5

Addition Marble Adding