ICS 212
Program Structure
William McDaniel Albritton
M.S.

Memory Allocation
Numeric Systems
Decimal, Binary, Hexadecimal
Converting
Integer Representation
Character Representation

Numeric
Systems

Decimal (base 10)
Uses positional representation
Each digit corresponds to a power of
10 based on its position in the number
The powers of 10 increment from 0, 1,
2, etc.
as you move right to left
1,479 = 1 * 10
3
+ 4 * 10
2
+ 7 * 10
1
+ 9 *
10
0

Binary (base 2)
Two digits: 0, 1
To make the binary numbers more
readable,
the digits are often put in groups of 4
1010 = 1 * 2
3
+ 0 * 2
2
+ 1 * 2
1
+ 0 * 2
0
= 8 + 2
= 10 decimal
1100 1001 = 1 * 2
7
+ 1 * 2
6
+ 1 * 2
3
+ 1
* 2
0
= 128 + 64 + 8 + 1
= 201 decimal

Shorter and easier to read than binary
16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C,
D, E, F
“0x” often precedes hexadecimal numbers
0x123 = 1 * 16
2
+ 2 * 16
1
+ 3 * 16
0
= 1 * 256 + 2 * 16 +
3 * 1
= 256 + 32 +
3
= 291 decimal
Hexadecimal (base 16)

Hexadecimal (base 16)
Another example
0xABC = A * 16
2
+ B * 16
1
+ C *
16
0
= 10 * 256 + 11 * 16 +
12 * 1
= 2560 + 176 +
12
= 2748 decimal

0000
0
0
0001
1
1
0010
2
2
0011
3
3
0100
4
4
0101
5
5
0110
6
6
0111
7
7
Binar
y
Decim
al
Hexadeci
mal

1000
8
8
1001
9
9
1010
10
A
1011
11
B
1100
12
C
1101
13
D
1110
14
E
1111
15
F
10000
16
10
Binar
y
Decim
al
Hexadeci
mal

Converting
From binary or hex to decimal
Use positional representation as
shown previously
From decimal to binary (or hex)
Keep dividing by 2 (or 16)
Remainders give the digits, starting
from lowest power

Converting
From binary to hex (or vice
versa)
Replace each set of four binary
digits by the corresponding
hexadecimal digit (or vice versa)

Convert Decimal to Binary
22 decimal = 10110 binary
Calculations:
2 |22 r. 0
2 |11 r. 1
2 |
5 r. 1
2 |
2 r. 0
2 |
1 r. 1
0

Convert Decimal to Binary
22 decimal = 10110 binary
Calculations:
Write down powers of 2
Subtract the largest power of 2 that is less than
the number
Add a 1 if can subtract, and a 0 if cannot
22
6
2
32
16
8
4
2
1
0
1
0
1
1
0

Other Bases
Base 8 (octal number system)
123 = 1 * 8
2
+ 2 * 8
1
+ 3 * 8
0
= 1 * 64 + 2 * 8 + 3 * 1
= 64 + 16 + 3
= 83 decimal

Other Bases

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- Spring '18
- Binary numeral system, Shorter, Keep, Remainders