question
Tutor Faith
8_bit_2s_complement.pdf
LDU – Maths, Stats & Numeracy Support
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How to convert decimal numbers to 8 bit 2’s complement If you are not sure how to convert decimal numbers to 8 bit 2’s complement form then have a look at this short video tutorial by PCC videos: http://www.youtube.com/watch?v=WrSMzaEkrO4 Here’s an example: Convert (– 47) into 8 bit 2’s complement Step 1) change the decimal number to binary 101111 Step 2) ensure the number is 8 bit by adding zero’s to the left hand side 00101111 Step 3) invert the number by changing all the 1’s to zero and all the zeros to 1 11010000 Step 4) add 1 to the right hand side 11010001 So the final answer is – 47 = 11010001 Now try these:‐ a) Convert the decimal number (– 5) into 8 bit 2’s complement b) Change (– 21) into 8 bit 2’s complement c) Express (– 67) as an 8 bit 2’s complement number
A N SW
ER S
a) 11111011
b ) 11101011
c) 10111101
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Binary subtraction using 8 bit 2’s complement
Computers do not manage direct subtraction very well. We can get round this problem by adding negative numbers when they are in 8 bit 2’s complement form. Here’s an example: 150 ‐ 47 Step 1) Convert the positive number into binary making sure it is 8 bits long, if it is too short just add zeros to the left hand side. 150 = 10010110 Step 2) Convert the negative number into 8 bits 2’s complement form. DO NOT convert the positive number. ‐ 47 = 11010001 Step 3) Add the numbers together using binary addition. 10010110 + 11010001 101100111 Step 4) Ignore any overflow: If you have a 9 bit number as your final answer, ignore the biggest place value on the left hand side so that your answer is 8 bits long. 101100111 So the final answer is 01100111 Now try these:‐ 1) 15 – 5 2) 77 ‐ 21 3) 100 – 67 AN
SW ER
S
1) 00001010
2) 00111000
3) 00100001
