Name: __________ Grade: __________ Title: Converting binary numbers to decimal O
ID: 3661528 • Letter: N
Question
Name: __________ Grade: __________
Title: Converting binary numbers to decimal
OBJECTIVES
In this iLab, you will develop an algorithm to convert binary numbers to decimal numbers, then apply the algorithm to several binary numbers to obtain their decimal equivalent.
II. PROCEDURE
The process of converting a 4-bit binary number to its decimal equivalent is demonstrated in the following steps.
Step 1: For each bit position, write down the base, 2, raised to the power of that bit position. For a 4-bit number, this would be as follows.
23222120
Step 2: Below each bit position, convert the power of 2 to its decimal value.
23 22 21 20
8 4 2 1
Step 3: Below the decimal weights, write down the binary number that will be converted. For example, use 1101.
23 22 21 20
8 4 2 1
1 1 0 1
Step 4: In each position, multiply the decimal weight by the binary number (i.e., 8 x 1 = 8, 4 x 1 = 4).
8 4 2 1
X X X X
1 1 0 1
= = = =
8 4 0 1
Step 5: Sum the numbers.
8 + 4 + 0 + 1 = 13
Therefore, the 4-bit number 1101 base 2 (binary) is equivalent to 13 base 10 (decimal).
Problems:
Using the process described above, convert the following 4-bit binary numbers to their decimal equivalents. Record your results.
0011 =
1100 =
Fill in the missing binary or decimal values in the following table.
Binary Bit 3
Binary Bit 2
Binary Bit 1
Binary Bit 0
Decimal
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
1
0
0
0
0
8
1
0
1
0
1
0
0
12
1
1
1
13
1
1
1
15
Extend the process described above and convert the following 8-bit binary numbers to their decimal equivalent. Record your results.
00010011 =
01011001 =
What is the largest binary number that can be generated in 8-bit binary? How did you arrive at this result?
In your own words, describe the process of converting a binary number into its decimal equivalent. This is the algorithm of converting a binary number to its decimal equivalent.
Rename your iLab document to FiLastNameLab1-1.docx. Upload the completed iLab to the weekly iLab Dropbox.
Binary Bit 3
Binary Bit 2
Binary Bit 1
Binary Bit 0
Decimal
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
1
0
0
0
0
8
1
0
1
0
1
0
0
12
1
1
1
13
1
1
1
15
Explanation / Answer
1.Converting 0011 to decimal
Step 1: For each bit position, write down the base, 2, raised to the power of that bit position
23 22 21 20
Step 2: Below each bit position, convert the power of 2 to its decimal value.
23 22 21 20
8 4 2 1
Step 3: Below the decimal weights, write down the binary number that will be converted
23 22 21 20
8 4 2 1
0 0 1 1
Step 4: In each position, multiply the decimal weight by the binary number
8 4 2 1
X X X X
0 0 1 1
= = = =
0 0 2 1
Step 5: Sum the numbers
0+ 0 + 2 + 1 =3
Therefore, the 4-bit number 0011 base 2 (binary) is equivalent to 3 base 10 (decimal).
2.Similariry for 1100
23 22 21 20
8 4 2 1
1 1 0 0
Next Step:
8 4 2 1
X X X X
1 1 0 0
=8+4+0+0
=12
Therefore, the 4-bit number 1100 base 2 (binary) is equivalent to 12 base 10 (decimal)
3.
Binary Bit
3
Binary Bit
2
Binary Bit
1
Binary Bit
0
Decimal
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
4
0
1
1
0
6
1
0
0
0
8
1
0
1
0
10
1
1
0
0
12
1
1
0
1
13
1
1
1
1
15
4.Coverting 8 Bit binary number to decimal:
Step 1: For each bit position, write down the base, 2, raised to the power of that bit position
27 26 25 2423 22 21 20
Step 2: Below each bit position, convert the power of 2 to its decimal value.
27 26 25 2423 22 21 20
128 64 32 16 8 4 2 1
Step 3: Below the decimal weights, write down the binary number that will be converted
27 26 25 2423 22 21 20
128 64 32 16 8 4 2 1
0 0 0 1 0 0 1 1
Step 4: In each position, multiply the decimal weight by the binary number
128 64 32 16 8 4 2 1
X X X X X X X X
0 0 0 1 0 0 1 1
= = = = = = = =
0 0 0 16 0 0 2 1
Step 5: Sum the numbers
16+ 2 + 1 =19
Therefore, the 8-bit number 00010011 base 2 (binary) is equivalent to 19 base 10 (decimal).
5.
Simalarily for converting 01011001 to decimal
128 64 32 16 8 4 2 1
X X X X X X X X
0 1 0 1 1 0 1 1
= = = = = = = =
0 64 0 16 8 0 2 1
Sum=64+16+8+2+1=91
Therefore, the 8-bit number 01011011 base 2 (binary) is equivalent to 91 base 10 (decimal).
6. Largest binary number generated in 8 bit is 11111111 because as for converting binary number to decimal we multiply each bit with the respective power of 2 according to bit number and if all the bits are 1 then we will get the maximum result.
Maximum 8 bit number 11111111 in decimal =128+64+32+16+8+4+2+1=255
7. Algorithm of converting binary to decimal
1. Write down the binary number bitwise with least significant bit as bit 0.
2. Multiply each bit with 2 being raised to power equal to the bit number of that bit as 20 for bit 0 and 21 with bit 1 and so on.
3. Add all the numbers generated after step 2 and we will get the decimal number reprsentation of the binary number.
Binary Bit
3
Binary Bit
2
Binary Bit
1
Binary Bit
0
Decimal
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
4
0
1
1
0
6
1
0
0
0
8
1
0
1
0
10
1
1
0
0
12
1
1
0
1
13
1
1
1
1
15
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