Vocabulary

Binary digit – can be 0 or 1

Computer Memory

Computers encode and store information as a sequence of bits. This diagram shows how the letter A is encoded.

Reviewing Decimal Numbers

Decimal numbers are base 10. A decimal digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Place Value of Decimal Numbers uses powers of 10.

106	105	104	103	102	101	100
1,000,000	100,000	10,000	1,000	100	10	1

Binary Numbers

Binary numbers are base 2. A binary digit can be 0 or 1

Place Value of Binary Numbers uses powers of 2.

26	25	24	23	22	21	20
64	32	16	8	4	2	1

Use the place value table to convert from binary to decimal.

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Example 1: Convert the binary number 1011 to decimal.

64	32	16	8	4	2	1
			1	0	1	1
			1 × 8 = 8	0 × 4 = 0	1 × 2 = 2	1 × 1 = 1
			8  +	0  +	2  +	1 =    11

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Example 2: Convert the binary number 110110 to decimal.

64	32	16	8	4	2	1
	1	1	0	1	1	0
	1 × 32 = 32	1 × 16 = 16	0 × 8 = 0	1 × 4 = 4	1 × 2 = 2	0 × 1 = 0
	32  +	16  +	0  +	4  +	2  +	0 =    54

Adding Binary Numbers

Adding binary numbers is just like adding decimal numbers, except that you use the binary addition table.

0 + 0 =	0
0 + 1 =	1
1 + 0 =	1
1 + 1 =	10
1 + 1 + 1 =	11

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Example 1: Add 101 + 10

1	0	1
+	1	0
1	1	1

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Example 2: Add 1101 + 11

When you add 1 + 1, you need to carry 1 to the next place.

	1	1		← carry digits
1	0	1	1
+		1	1
1	1	1	0