CS114 Lab: Decimal, Binary, Hexadecimal Systems

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Representation of Numbers and the Binary System

Inside a computer, numbers are represented using the Binary System, as you know.

Learn the first 10 powers of 2:

power	2 to the power (in decimal)
0	1
1	2
2	4
3	8
4	16
5	32
6	64
7	128
8	256
9	512
10	1024

Decimal and Binary values from 0 to 15:

Decimal Value	Binary Value
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111

Binary to Decimal

You already know how to do this. As a reminder, number 10011 in binary is the same as 19 in decimal, because:

1*16 + 0*8 + 0*4 + 1*2 + 1*1 = 19

Convert the following binary numbers into decimal:
1. 00000000 -->
2. 00001111 -->
3. 01101011 -->
4. 11111111 -->
5. 00000000 00000000 -->
6. 00000000 11111111 -->
7. 00000010 01100011 -->
8. 00000001 01100011 -->

Decimal to Binary

To convert a decimal number to the binary equivalanr, we need to express the decimal number as a sum of powers of 2. Based on this, write down an 1 for every power that appears in the sume, and a 0 for each that does not. Pad it up with leading zeros so that you get a whole number of bytes. Here is an example:

113(decimal) = 1*64 + 1*32 + 1*16 + 1*1 = 

               1*64 + 1*32 + 1*16 + 0*8 + 0*4 + 0*2 + 1*1 --> 01110001 (binary)

Convert the following decimal numbers into binary:
1. 70 -->
2. 25 -->
3. 49 -->
4. 63 -->
5. 231 -->
6. 513 -->
7. 623 -->
8. 640 -->