HWD101Lab5AnsUnhidden

HWD101Lab5AnsUnhidden - Hardware101 Fall 2009 Lab week...

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Hardware101 –Fall 2009 Lab – week 5 ANSWERS Binary Arithmetic and Conversions – practice only 1. Perform the following additions in binary: 1011 + 11101101 + 10101110 + 1011 10101001 101001 10 110 110010110 110101011 2. Perform the following subtractions in binary using the method of “2’s Complement”. 1110 - 10111001 - 111010101110 – 1001 10010001 11011100 0101 | 00101000 1 110111010010 3. How many different addresses can be assigned with an 8-bit address bus? 2 to the power of 8 (256) 4. How can you tell at a glance whether a binary number is even or odd? If the rightmost digit is a “1” the number is odd.
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5. Perform the following conversions: From: To Binary: 11101101 Decimal = 237 Decimal: 576 Binary = 1001000000 Octal: 461 Binary = 100110001 Binary 10101011 Octal = 253 Hexadecimal: 2CE Decimal = 718 Binary 110111111011 Hex = DFB Octal: 37 Decimal = 31
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In General: Binary Arithmetic Arithmetic operations (addition, subtraction, multiplication and division) can be carried out on binary numbers in the same way as decimal numbers. Since there are only two digits, the operations are simpler. Binary Addition When you add two binary digits, there are just the following four combinations: 0 0 1 1 +0 +1 +0 + 1 -- -- -- --- 0 1 1 10 | ---- carry out to next position> The result of adding two 1s is 2, which is 10 in binary notation. The 1 in (10) 2 represents the carry digit and it is added to the next higher binary position. This is very similar to the decimal addition of 8 and 4: 8 + 4 -- 12 carry --------- | The 1 represents the carry digit, while 2 is recorded in the units position. Since the 1 is in the tens position, its value is 10.
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