Avalon Brown - 2.3.4.A TwoComplementArithmetic
Avalon Brown - 2.3.4.A TwoComplementArithmetic
Avalon Brown - 2.3.4.A TwoComplementArithmetic
"to attempt to take [a number] away from a number less than itself is ridiculous."
Even Augustus DeMorgan, author of the famed DeMorgan Theorems, thought that numbers
less than zero were unimaginable.
We all know now that negative numbers do exist. We learned about them in the third grade,
and we use them every day. A golfer who scores a 67 on a par 72 course would describe her
score as 5 under par, or -5. Likewise, in the northern climate of the United States, the winter
temperatures can drop to 10° below zero, or -10° Fahrenheit.
If negative decimal numbers exist and you can convert a decimal number into its binary
equivalent, then there must be a way to represent negative binary numbers.
In this activity you will learn how to express numbers in their 8-bit - 2’s complement binary
equivalent. You will use these equivalencies to perform simple addition and subtraction.
Equipment
● Calculator (preferably one with a number base conversion feature)
Procedure
1) Express the following decimal numbers as their 8-bit - 2’s complement binary
equivalent.
a) 114 (10) = 01110010 (2)
2) Express the following 8-bit - 2’s complement binary number as their decimal
equivalent.
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.3.4 Two’s Complement Arithmetic – Page 1
a) 11011001 (2) = -39 (10)
3) Perform each of the following additions in 2’s complement form. Check your answers
by converting the 2’s complement binary numbers into their decimal equivalents and
adding.
a)
00101011
b)
11100001
c)
11001001
d)
11000000
a)
00100101
b)
00001000
c)
00010110
d)
11100110
Conclusion
1) What is the largest positive and smallest negative decimal number that can be
expressed as an 8-bit - 2’s complement binary number?
127 and -128
a) 00110001
b) 11001111
c) 01100110