Binary Worksheet for AP CSP

Flashcards covering powers of two, binary to decimal conversion, decimal to binary conversion, 4-bit overflow addition, and bit requirements from the AP CSP Binary Worksheet.

Based on the AP CSP powers of two table, what are the values of $2^n$ for exponents $n = 0$ through $10$?

$n=0: 1$, $n=1: 2$, $n=2: 4$, $n=3: 8$, $n=4: 16$, $n=5: 32$, $n=6: 64$, $n=7: 128$, $n=8: 256$, $n=9: 512$, $n=10: 1024$

How is the binary number $1011_2$ converted to decimal?

$$(1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) = 8 + 0 + 2 + 1 = 11_{10}$$

How is the binary number $11010_2$ converted to decimal?

$$(1 \times 16) + (1 \times 8) + (0 \times 4) + (1 \times 2) + (0 \times 1) = 16 + 8 + 0 + 2 + 0 = 26_{10}$$

How is the binary number $100101_2$ converted to decimal?

$$(1 \times 32) + (0 \times 16) + (0 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1) = 32 + 4 + 1 = 37_{10}$$

How is the binary number $011111_2$ converted to decimal?

$$(0 \times 32) + (1 \times 16) + (1 \times 8) + (1 \times 4) + (1 \times 2) + (1 \times 1) = 16 + 8 + 4 + 2 + 1 = 31_{10}$$

How is the decimal number $13_{10}$ converted to binary?

$$8 + 4 + 1 = 1101_2$$

How is the decimal number $22_{10}$ converted to binary?

$$16 + 4 + 2 = 10110_2$$

How is the decimal number $31_{10}$ converted to binary?

$$16 + 8 + 4 + 2 + 1 = 11111_2$$

How is the decimal number $45_{10}$ converted to binary?

$$32 + 8 + 4 + 1 = 101101_2$$

What is the largest value that can be represented with 4 bits?

$15_{10}$ ($1111_2$)

What are the five standard binary addition rules?

$0 + 0 = 0$, $0 + 1 = 1$, $1 + 0 = 1$, $1 + 1 = 10$ ($0$, carry the $1$), and $1 + 1 + 1 = 11$ ($1$, carry the $1$)

What is the result of the binary addition $0101_2 (5) + 0011_2 (3)$?

$1000_2$ ($8_{10}$)

What is the result and register value for the 4-bit addition $1010_2 (10) + 0111_2 (7)$?

The exact result is $10001_2$ ($17_{10}$). Since it requires 5 bits, an overflow occurs and the 4-bit register holds $0001_2$.

What is the result and register value for the 4-bit addition $1111_2 (15) + 0001_2 (1)$?

The exact result is $10000_2$ ($16_{10}$). Since it requires 5 bits, an overflow occurs and the 4-bit register holds $0000_2$.

What is the result and register value for the 4-bit addition $1001_2 (9) + 1001_2 (9)$?

The exact result is $10010_2$ ($18_{10}$). Since it requires 5 bits, an overflow occurs and the 4-bit register holds $0010_2$.

What is a register value as defined in the worksheet?

A register value is the data currently held within a specific storage location in a computer's processor (CPU), known as a register.

How many unique values can be represented with $5$ bits?

$5$ bits can represent $2^5 = 32$ unique values.

How many bits are required to represent at least $6$ distinct patterns?

$3$ bits are required ($2^3 = 8$), because $2$ bits only provide $4$ patterns.

How many bits are needed to represent scores from $0$ to $100$ inclusive ($101$ values)?

$7$ bits are needed ($2^7 = 128$).

Why are $6$ bits not enough to represent scores from $0$ to $100$ inclusive?

$6$ bits are not enough because $2^6 = 64$, which is less than the $101$ required values.