Binary Adder-Subtractor
The subtraction of binary numbers can be done most conveniently by means of complements as discussed in Sec. 3-2. Remember that the subtraction A - B can be done by taking the 2's complement of B and adding it to A. The 2's complement can be obtained by taking the 1' s complement and adding one to the least significant pair of bits. The 1's complement can be implemented with inverters and a one can be added to the sum through the input carry.
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The addition and subtraction operations can be combined into one common circuit by including an exclusive-OR gate with each full-adder. A 4-bit adder-subtractor circuit is shown in Fig. 4-7. The mode input M controls the operation. When M = 0 the circuit is an adder and when M = 1 the circuit becomes a subtractor. Each exclusive-OR gate receives input M and one of the inputs of B. When M = 0, we have B a1 0 = B. The full-adders receive the value of B, the input carry is O, and the circuit performs A plus B. When M = 1, we have B a1 1 = B' and C0 = 1. The B inputs are all complemented and a 1 is added through the input carry. The circuit performs the operation A plus the 2's complement of B. For unsigned numbers, this gives A - B if A '" B or the 2's complement of (8 - A) if A < B. For signed numbers, the result is A - B provided that there Is no overflow.
Frequently Asked Questions
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Ans: To implement the add microoperation with hardware, we need the registers
that hold the data and the digital component that performs the arithmetic
addition. The digital circuit that forms the arithmetic sum of two bits and a
previous carry is called a full-adder . view more..
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Ans: The operation of a memory unit was described in Sec. 2-7. The transfer of
information from a memory word to the outside environment is called a read
operation. view more..
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Ans: A bus system can be constructed with three-state gates instead of multiplexers.
A three-state gate is a digital circuit that exhibits three states. Two of the states
are signals equivalent to logic 1 and 0 as in a conventional gate. The third state
is a high-impedance state. view more..
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Ans: The subtraction of binary numbers can be done most conveniently by means
of complements as discussed in Sec. 3-2. Remember that the subtraction A - B
can be done by taking the 2's complement of B and adding it to A. The 2's
complement can be obtained by taking the 1' s complement and adding one to
the least significant pair of bits. The 1's complement can be implemented with
inverters and a one can be added to the sum through the input carry. view more..
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Ans: The increment microoperation adds one to a number in a register. For example,
if a 4-bit register has a binary value 0110, it will go toO! II afterit is incremented.
This microoperation is easily implemented with a binary counter view more..
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Ans: Logic microoperations specify binary operations for strings of bits stored in
registers. These operations consider each bit of the register separately and treat
them as binary variables. For example, the exclusive-OR microoperation with
the contents of two registers . view more..
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Ans: There are 16 different logic operations that can be performed with two binary
variables. They can be determined from all possible truth tables obtained with
two binary variables as shown in Table 4-5. In this table, each of the 16 columns
F0 through F15 represents a truth table of one possible Boolean function for the view more..
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Ans: The hardware implementation of logic rnicrooperations requires that logic
gates be inserted for each bit or pair of bits in the registers to perform the
required logic function. Although there are 16 logic rnicrooperations, most
computers use only four-AND, OR, XOR (exclusive-OR), and complementfrom
which all others can be derived. view more..
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Ans: Logic microoperations are very useful for manipulating individual bits or a
portion of a word stored in a register. They can be used to change bit values,
delete a group of bits, or insert new bit values into a register. view more..
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Ans: The selective-set operation sets to 1 the bits in register A where there are
corresponding 1's in register B. It does not affect bit positions that have D's in
B. The following numerical example clarifies this operation. view more..
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Ans: Shift rnicrooperations are used for serial transfer of data. They are also used
in conjunction with arithmetic, logic, and other data-processing operations.
The contents of a register can be shifted to the left or the right. At the same
time that the bits are shifted, the first flip-flop receives its binary information
from the serial input view more..
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Ans: Instead of having individual registers performing the microoperations directly,
computer systems employ a number of storage registers connected to a common
operational unit called an arithmetic logic unit, abbreviated ALU. view more..
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Ans: In this chapter we introduce a basic computer and show how its operation can
be
puter
specified with register
is defined by its internal
transfer
registers,
statements.
the limirlg
The otganization
and control
of
structure,
the comand
the set of instructions that It uses. The design of the computer is then
carried out in detall. Although the basic computer presented in this chap view more..
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Ans: An instruction code is a group of bits that instruct the computer to
perform a specific operation. It is usually divided into parts, each having its
own particular interpretation. The most basic part of an instruction code is its
operation part. The operation code of an instruction is a group of bits that
define such operations as add, view more..
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Ans: The simplest way to organize a computer is to have one processor register and
an instruction code format with two parts. The first part specifies the operation
to be performed and the second specifies an address. The memory address tells
the control where to find an operand in memory. This operand is read from
memory and used as the data to be operated on together with the data stored
in the processor register view more..
+
Ans: In this chapter we introduce a basic computer and show how its operation can
be
puter
specified with register
is defined by its internal
transfer
registers,
statements.
the limirlg
The otganization
and control
of
structure,
the comand
the set of instructions that It uses. The design of the computer is then
carried out in detall. Although the basic computer presented in this chapter is
very small compared to commercial computers, It has the advantage of being
simple enough so we can demonstrate the design process without too many
complications. view more..
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Ans: It is sometimes convenient to use the address bits of an instruction code not
as an address but as the actual operand. When the second part of an instruction
code specifies an operand, the instruction is said to have an immediate
operand. view more..
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Ans: Computer instructions are normally stored in consecutive memory locations
and are executed sequentially one at a time. The control reads an instruction
from a specific address in memory and executes it. It then continues by reading
the next instruction in sequence and executes it, and so on. view more..
Recommended Posts:
- DATA TYPES
- NUMBER SYSTEM
- CONVERSION - INTRODUCTION
- OCTAL AND HEXADECIMAL NUMBER CONVERSION
- OCTAL AND HEXADECIMAL NUMBER CONVERSION -2
- Introduction to Decimal Representation
- ALPHANUMERIC REPRESENTATION
- Complements
- Complements -2
- Subtraction of Unsigned Numbers
- Subtraction of Unsigned Numbers-2
- Fixed-Point Representation
- Integer Representation
- Arithmetic Addition
- ARITHMETIC SUBTRACTION
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