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Example 7.3
A 4-bit register contains the binary word 0101. Convert this to its decimal equivalent assuming a
straight binary code.
KNOWN 4-bit register
FIND Convert to base 10
ASSUMPTION Straight binary code
SOLUTION The content of the 4-bit register is the binary word 0101. This represents
0 Â 2
3
þ 1 Â 2
2
þ 0 Â 2
1
þ 1 Â 2
0
¼ 5
The equivalent of 0101 in decimal is 5.
7.4 TRANSMITTING DIGITAL NUMBERS: HIGH AND LOW SIGNALS
Electrical devices transmit binary code by using differing voltage levels. Because a bit can have a
value of 1 or 0, the presence of a particular voltage (call it HIGH) at a junction could be used to
represent a 1-bit value, whereas a different voltage (LOW) could represent a 0. Most simply, this
voltage can be affected by use of an open or closed switch using a flip-flop (see Chapter 6), such as
depicted in Figure 7.5a.
For example, a signal method common with many digital devices is a þ5 V form of TTL (true
transistor logic), which uses a nominal þ5 V HIGH/0 V LOW scheme for representing the value of a
bit. To avoid any ambiguity due to voltage fluctuations and provide for more precision, a voltage
level between þ2 and þ5.5 V is taken as HIGH and therefore a bit value of 1, whereas a voltage
between À0.6 and þ0.8 V is taken as LOW or a 0-bit value. But this scheme is not unique.
Binary numbers can be formed through a combination of HIGH and LOW voltages. Several
switches can be grouped in parallel to form a register. Such an M-bit register forms a number based on
the value of the voltages at its M output lines. This is illustrated in Figure 7.5b for a 4-bit register
forming the number 1010. So the bit values can be changed simply by changing the opened or closed
state of the switches that connect to the output lines. This defines a parallel form in which all of the bits
needed to form a word are available simultaneously. But another form is serial, where the bits are
separated in a time sequence of HIGH/LOW pulses, each pulse lasting for only one predefined time
duration, dt. This is illustrated in the pulse sequence of Figure 7.5c, which also forms the number 1010.
7.5 VOLTAGE MEASUREMENTS
Digital measurement devices consist of several components that interface the digital device with the
analog world. In particular, the digital-to-analog converter and the analog-to-digital converter are
discussed next. They form the major components of a digital voltmeter and an analog-to-digital/
digital-to-analog data acquisition system.
Digital-to-Analog Converter
A digital-to-analog converter is an M-bit digital device that converts a digital binary word into an
analog voltage (5–8). One possible scheme uses an M-bit register with a weighted resistor ladder
7.5 Voltage Measurements 271
14:43:49 Page 271
Example 7.3
A 4-bit register contains the binary word 0101. Convert this to its decimal equivalent assuming a
straight binary code.
KNOWN 4-bit register
FIND Convert to base 10
ASSUMPTION Straight binary code
SOLUTION The content of the 4-bit register is the binary word 0101. This represents
0 Â 2
3
þ 1 Â 2
2
þ 0 Â 2
1
þ 1 Â 2
0
¼ 5
The equivalent of 0101 in decimal is 5.
7.4 TRANSMITTING DIGITAL NUMBERS: HIGH AND LOW SIGNALS
Electrical devices transmit binary code by using differing voltage levels. Because a bit can have a
value of 1 or 0, the presence of a particular voltage (call it HIGH) at a junction could be used to
represent a 1-bit value, whereas a different voltage (LOW) could represent a 0. Most simply, this
voltage can be affected by use of an open or closed switch using a flip-flop (see Chapter 6), such as
depicted in Figure 7.5a.
For example, a signal method common with many digital devices is a þ5 V form of TTL (true
transistor logic), which uses a nominal þ5 V HIGH/0 V LOW scheme for representing the value of a
bit. To avoid any ambiguity due to voltage fluctuations and provide for more precision, a voltage
level between þ2 and þ5.5 V is taken as HIGH and therefore a bit value of 1, whereas a voltage
between À0.6 and þ0.8 V is taken as LOW or a 0-bit value. But this scheme is not unique.
Binary numbers can be formed through a combination of HIGH and LOW voltages. Several
switches can be grouped in parallel to form a register. Such an M-bit register forms a number based on
the value of the voltages at its M output lines. This is illustrated in Figure 7.5b for a 4-bit register
forming the number 1010. So the bit values can be changed simply by changing the opened or closed
state of the switches that connect to the output lines. This defines a parallel form in which all of the bits
needed to form a word are available simultaneously. But another form is serial, where the bits are
separated in a time sequence of HIGH/LOW pulses, each pulse lasting for only one predefined time
duration, dt. This is illustrated in the pulse sequence of Figure 7.5c, which also forms the number 1010.
7.5 VOLTAGE MEASUREMENTS
Digital measurement devices consist of several components that interface the digital device with the
analog world. In particular, the digital-to-analog converter and the analog-to-digital converter are
discussed next. They form the major components of a digital voltmeter and an analog-to-digital/
digital-to-analog data acquisition system.
Digital-to-Analog Converter
A digital-to-analog converter is an M-bit digital device that converts a digital binary word into an
analog voltage (5–8). One possible scheme uses an M-bit register with a weighted resistor ladder
7.5 Voltage Measurements 271