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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 8bit 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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View Full Document 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
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
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This note was uploaded on 05/17/2010 for the course CTY HWD101 taught by Professor Parker during the Winter '10 term at Seneca.
 Winter '10
 parker

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