Chapter 4, Problem 4.1QAP

Convert each of the following decimal numbers to its binary equivalent.
(a) 37 (b) 93 (c) 129 (d) 355

Interpretation Introduction

(a)

Interpretation:

Decimal number 37 should be converted into the binary number.

Concept introduction:

The decimal number are base 10 numbering system. There are ten symbols use in 10 base system. They are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The binary numbers are base 2 numbering system. Binary only use two symbols which are 0 and 1.

When converting decimal number to binary number; divide the decimal number by 02 first. Then write down the result underneath and write the remainder on the right-hand side (always remainder will be 0 or 1). Continue the dividing and writing down the remainders until the result of the division is equal to zero.

Answer to Problem 4.1QAP

100101

Explanation of Solution

$\begin{array}{l}2\overline{)37-1}\\ 2\overline{)18-0}\\ 2\overline{)9-1}\\ 2\overline{)4-0}\\ 2\overline{)2-0}\\ 2\overline{)1-1}\\ \text{ 0}\end{array}$ 100101

Interpretation Introduction

(b)

Interpretation:

Decimal number 93 should be converted into the binary number.

Concept introduction:

The decimal number are base 10 numbering system. There are ten symbols use in 10 base system. They are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The binary numbers are base 2 numbering system. Binary only use two symbols which are 0 and 1.

When converting decimal number to binary number; divide the decimal number by 02 first. Then write down the result underneath and write the remainder on the right-hand side (always remainder will be 0 or 1). Continue the dividing and writing down the remainders until the result of the division is equal to zero.

Answer to Problem 4.1QAP

1011101

Explanation of Solution

$\begin{array}{l}2\overline{)93-1}\\ 2\overline{)46-0}\\ 2\overline{)23-1}\\ 2\overline{)11-1}\\ 2\overline{)5-1}\\ 2\overline{)2-0}\\ 2\overline{)1-1}\\ \text{ 0 }\end{array}$ 1011101

Interpretation Introduction

(c)

Interpretation:

Decimal number 129 should be converted into the binary number.

Concept introduction:

The decimal number are base 10 numbering system. There are ten symbols use in 10 base system. They are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The binary numbers are base 2 numbering system. Binary only use two symbols which are 0 and 1.

When converting decimal number to binary number; divide the decimal number by 02 first. Then write down the result underneath and write the remainder on the right-hand side (always remainder will be 0 or 1). Continue the dividing and writing down the remainders until the result of the division is equal to zero.

Answer to Problem 4.1QAP

10000001

Explanation of Solution

$\begin{array}{l}2\overline{)129-1}\\ 2\overline{)64-0}\\ 2\overline{)32-0}\\ 2\overline{)16-0}\\ 2\overline{)8-0}\\ 2\overline{)4-0}\\ 2\overline{)2-0}\\ \text{2}\overline{)1-1}\\ \text{ 0}\end{array}$ 10000001

Interpretation Introduction

(d)

Interpretation:

Decimal number 355 should be converted into the binary number.

Concept introduction:

The decimal number are base 10 numbering system. There are ten symbols use in 10 base system. They are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The binary numbers are base 2 numbering system. Binary only use two symbols which are 0 and 1.

When converting decimal number to binary number; divide the decimal number by 02 first. Then write down the result underneath and write the remainder on the right-hand side (always remainder will be 0 or 1). Continue the dividing and writing down the remainders until the result of the division is equal to zero.

Answer to Problem 4.1QAP

101100011

Explanation of Solution

$\begin{array}{l}2\overline{)355-1}\\ 2\overline{)177-1}\\ 2\overline{)88-0}\\ 2\overline{)44-0}\\ 2\overline{)22-0}\\ 2\overline{)11-1}\\ 2\overline{)5-1}\\ \text{2}\overline{)2-0}\\ 2\overline{)1-1}\\ \text{ 0}\end{array}$ 101100011