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EDPT practice questions

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Question 1Electronic data processing aptitude

In electronic data processing, which unit represents the smallest addressable storage location that a program can reference by name?

  1. A nibble
  2. A bit
  3. A byte Correct answer.
  4. A block

Explanation

Main memory is organized into addressable units, and in nearly all EDP systems the addressable unit is the byte, which is itself composed of eight bits. A bit is addressable only through bit-manipulation instructions, not as a named memory location, and a block is a larger transfer unit.

Question 2Electronic data processing aptitude

A data-processing operator converts the decimal value 157 to binary. Which bit pattern is correct?

  1. 10011011
  2. 11001101
  3. 10011100
  4. 10011101 Correct answer.

Explanation

157 equals 128 + 16 + 8 + 4 + 1, which sets bits 7, 4, 3, 2, and 0, giving 10011101. Checking the place values of 128, 64, 32, 16, 8, 4, 2, and 1 confirms that only those positions are on.

Question 3Electronic data processing aptitude

In a batch-processing payroll run, records are grouped and processed at a scheduled time rather than as each employee's timecard arrives. Which characteristic is the defining feature of this mode of EDP?

  1. Guaranteed sub-second response time
  2. Grouping transactions for deferred processing Correct answer.
  3. Immediate user interaction with each transaction
  4. Continuous online validation against a master file

Explanation

Batch processing collects transactions into a group and runs them against the master file at a scheduled interval, so latency between input and output is expected. Interactive, online, and real-time modes are distinguished by immediate processing of each transaction as it arrives.

Question 4Electronic data processing aptitude

A file stores fixed-length records of 200 bytes each, and a disk block holds 4,096 bytes. How many complete records fit in one block, and how many unused bytes remain?

  1. 20 records, 0 bytes unused
  2. 19 records, 296 bytes unused
  3. 20 records, 96 bytes unused Correct answer.
  4. 21 records, 96 bytes unused

Explanation

Dividing 4,096 by 200 gives 20 complete records with a remainder, since 20 × 200 = 4,000. The leftover space is 4,096 − 4,000 = 96 bytes, which cannot hold another full record.

Question 5Electronic data processing aptitude

Which data-processing term describes a single character encoded in a standard such as ASCII?

  1. A record
  2. A byte Correct answer.
  3. A file
  4. A field

Explanation

In ASCII each character is encoded in one 7- or 8-bit byte, so the byte is the unit that holds a single character. Fields, records, and files are progressively larger logical groupings built from characters.

Question 6Electronic data processing aptitude

A program reads a numeric field stored in packed decimal format. What does packed decimal represent?

  1. A hexadecimal-only encoding of integers
  2. A binary floating-point mantissa
  3. One decimal digit per 8-bit byte
  4. Two decimal digits per byte, with a sign nibble Correct answer.

Explanation

Packed decimal stores two decimal digits in each byte, one per nibble, and reserves a final nibble for the sign. This is more compact than zoned decimal, which stores one digit per byte.

Question 7Electronic data processing aptitude

Which statement correctly describes the role of a program counter (instruction pointer) during EDP program execution?

  1. It stores the operand being processed by the ALU
  2. It caches recently accessed data blocks
  3. It records the number of clock cycles elapsed
  4. It holds the address of the next instruction to fetch Correct answer.

Explanation

The program counter holds the address of the next instruction to be fetched, and it is incremented or set by branch instructions to control execution flow. Operands and results pass through registers such as the accumulator, while caches hold data separately.

Question 8Electronic data processing aptitude

A data-entry clerk needs to verify that a nine-digit account number was keyed correctly by adding a check digit. What is the primary purpose of a check digit in EDP data entry?

  1. To encrypt the account number
  2. To detect transcription errors such as single-digit mistakes Correct answer.
  3. To compress the number for storage
  4. To identify the record's owner

Explanation

A check digit is computed from the other digits by a fixed rule and appended, so a keying error usually breaks the rule and is caught during validation. It detects errors but does not provide security, compression, or ownership information.

Question 9Electronic data processing aptitude

A sequential file of 500,000 customer records is searched for a single account. On average, how many record comparisons does a linear search require, and how does a binary search compare?

  1. About 19 comparisons for linear versus about 250,000 for binary
  2. About 250,000 comparisons for linear versus about 250,000 for binary
  3. About 500,000 comparisons for linear versus about 250,000 for binary
  4. About 250,000 comparisons for linear versus about 19 for binary Correct answer.

Explanation

A linear search checks records one by one, averaging about half the file, or roughly 250,000 comparisons. A binary search halves the search interval each step, requiring about log2(500,000), which is approximately 19 comparisons.

Question 10Electronic data processing aptitude

A file of employee records must be sorted by department code, and within each department by surname. Which sorting approach produces the required ordering?

  1. Sort by department code only
  2. Sort by department code, then sort the result by surname using a stable sort
  3. Sort by surname, then sort the result by department code using a stable sort Correct answer.
  4. Sort by surname only

Explanation

The secondary key must be sorted first, then the primary key with a stable sort so that records sharing a department keep their surname order. Sorting by department first and then by surname would destroy the grouping by department.

Question 11Electronic data processing aptitude

An 8-bit register holds the two's complement value 11110110. What decimal value does it represent?

  1. -10 Correct answer.
  2. -9
  3. -246
  4. 246

Explanation

The leading 1 indicates a negative value. Inverting the bits gives 00001001 (9) and adding 1 gives 10, so the value is -10; equivalently, 11110110 equals 256 − 10 in unsigned terms.

Question 12Electronic data processing aptitude

A validation routine checks that a birth-date field contains a value no later than today and no earlier than 120 years ago. Which type of validation is this?

  1. Format check
  2. Existence check
  3. Range check Correct answer.
  4. Check digit

Explanation

A range check verifies that a value falls between defined lower and upper limits, here a valid birth-date window. Format checks examine the shape of the data, existence checks confirm a value is present, and check digits detect transcription errors.

Question 13Electronic data processing aptitude

In a relational data-processing system, a table's primary key must satisfy which condition?

  1. It must be the last column defined
  2. It must reference another table's key
  3. It must be a numeric field
  4. It must uniquely identify each row and contain no nulls Correct answer.

Explanation

A primary key enforces entity integrity: every row has a value and no two rows share the same key value. It may be alphabetic or composite, and a foreign key, not the primary key, references another table.

Question 14Electronic data processing aptitude

A sequential master file is updated nightly by a transaction file sorted in the same key order. Why must the transaction file be sorted before the update run?

  1. To reduce the size of the transaction file
  2. To allow both files to be read in a single synchronized pass Correct answer.
  3. To encrypt the transaction records
  4. To remove duplicate records automatically

Explanation

In sequential update, the master and transaction files are read forward together, matching keys as they advance. Sorting the transaction file in master-key order makes this single synchronized pass possible without rewinding either file.

Question 15Electronic data processing aptitude

A hexadecimal dump shows the byte value 4F. What is its decimal equivalent?

  1. 64
  2. 79 Correct answer.
  3. 95
  4. 415

Explanation

Hexadecimal 4F equals 4 × 16 + 15, since F represents 15, giving 64 + 15 = 79. Each hex digit is weighted by a power of 16 from the right.

Question 16Electronic data processing aptitude

An EDP system uses parity checking on transmitted bytes. What limitation does a single parity bit have?

  1. It requires the receiver to know the original message
  2. It detects an odd number of flipped bits but misses an even number of flips Correct answer.
  3. It cannot detect any transmission errors
  4. It corrects all single-bit errors automatically

Explanation

A single parity bit makes the count of 1s odd or even, so any odd number of bit flips changes the parity and is detected. Two flips leave the parity unchanged and pass undetected, and parity cannot locate or correct the error.

Question 17Electronic data processing aptitude

A file contains 1,024 records of 512 bytes each. Expressed in kilobytes using 1 KB = 1,024 bytes, what is the file size?

  1. 512 KB Correct answer.
  2. 2,048 KB
  3. 1,024 KB
  4. 256 KB

Explanation

Multiplying 1,024 records by 512 bytes gives 524,288 bytes. Dividing by 1,024 bytes per kilobyte yields 512 KB, since each kilobyte holds two records.

Question 18Electronic data processing aptitude

In a database, a foreign key in an order table references the customer table. What does the foreign key constraint enforce?

  1. That customer records cannot be deleted for any reason
  2. That each order's customer reference matches an existing customer Correct answer.
  3. That every order value is unique
  4. That orders are stored in customer-number order

Explanation

A foreign key enforces referential integrity: a value in the referencing column must exist as a key value in the referenced table. Deletion of a referenced customer is restricted or cascaded by the rule, not forbidden in all cases, and physical ordering is not implied.

Question 19Electronic data processing aptitude

A transaction-processing system must record a funds transfer so that either both the debit and the credit occur or neither does. Which property of transactions does this describe?

  1. Durability
  2. Isolation
  3. Atomicity Correct answer.
  4. Consistency

Explanation

Atomicity treats a transaction as an indivisible unit: all its operations commit together or are rolled back together. Durability concerns permanence after commit, isolation concerns concurrent visibility, and consistency concerns valid state transitions.

Question 20Electronic data processing aptitude

A program contains the loop: FOR I = 1 TO 10 STEP 2. How many times does the loop body execute?

  1. 6
  2. 10
  3. 4
  4. 5 Correct answer.

Explanation

The counter takes the values 1, 3, 5, 7, and 9 before exceeding 10, giving five iterations. Counting from 1 to 10 by twos yields five values, and the next value, 11, terminates the loop.

Question 21Electronic data processing aptitude

A company's data-processing workload requires very high volumes of sequential record processing with minimal per-record cost, and results are needed only by the next morning. Which processing mode best fits?

  1. Batch processing Correct answer.
  2. Online transaction processing
  3. Real-time processing
  4. Interactive time-sharing

Explanation

High-volume sequential work with overnight turnaround is the classic case for batch processing, which maximizes throughput and minimizes per-record overhead. Real-time, interactive, and online modes are justified when immediate per-transaction response is required.

Question 22Electronic data processing aptitude

A record layout places a 10-byte name, a 4-byte integer, and a 1-byte code consecutively with no padding. What is the offset of the code field from the start of the record?

  1. 10
  2. 4
  3. 15
  4. 14 Correct answer.

Explanation

Offsets count bytes before the field: the name occupies offsets 0 through 9 and the integer occupies 10 through 13. The code therefore begins at offset 14, which is the sum of the preceding field lengths.

Question 23Electronic data processing aptitude

A hash function maps 1,000 keys into 100 buckets. Assuming a uniform distribution, what is the expected number of keys per bucket, and what happens as the load factor rises?

  1. 100 keys per bucket, with fewer collisions as the load factor rises
  2. 10 keys per bucket, with collisions disappearing once the table is full
  3. 1 key per bucket, with constant performance regardless of load
  4. 10 keys per bucket, with more collisions and longer probe chains as the load factor rises Correct answer.

Explanation

Dividing 1,000 keys by 100 buckets gives an average of 10 keys per bucket. As the load factor increases, more keys share buckets, so collisions and the length of probe or chain searches grow, degrading lookup performance.

Question 24Electronic data processing aptitude

An indexed sequential file uses a sparse index over sorted records. What trade-off does the index introduce compared with a pure sequential file?

  1. Elimination of all sequential processing capability
  2. Slower access with no additional storage cost
  3. Guaranteed constant-time access regardless of file size
  4. Faster direct access at the cost of extra storage and maintenance for the index Correct answer.

Explanation

The index lets the system jump close to a record's position instead of scanning the whole file, so direct access improves. The cost is additional storage for index entries and the work of updating the index whenever records are inserted or deleted.

Question 25Electronic data processing aptitude

A system stores signed integers in 8-bit two's complement. Adding 100 and 50 produces a result that appears negative. What has occurred, and why?

  1. Overflow, because the true sum 150 exceeds the maximum representable value 127 Correct answer.
  2. Underflow, because the operands are both positive
  3. A rounding error introduced by the arithmetic unit
  4. A carry error, because two's complement cannot add positive numbers

Explanation

The 8-bit two's complement range is -128 to 127, so the true sum of 150 cannot be represented. The bit pattern wraps into the negative range, a condition called overflow, which must be detected by checking the sign of the result against the operands.

Question 26Electronic data processing aptitude

In an EDP installation, a field is described as having a zoned decimal format. How are the digits and sign stored in this format?

  1. Each digit occupies one byte, with the numeric value in the low-order four bits and the sign in the high-order four bits of the last byte. Correct answer.
  2. Each digit occupies one byte, and the sign is encoded by complementing all bits of the final byte.
  3. Each digit is stored as a separate character in ASCII, and the sign is implied by the presence of a minus character.
  4. Two digits are packed into each byte, and the sign is stored in a separate one-bit flag in the record header.

Explanation

Zoned decimal stores one decimal digit per byte, holding the digit value in the zone nibble or the numeric nibble depending on convention, with the sign overpunched in the zone nibble of the final byte. This makes it directly displayable but wasteful of storage compared with packed decimal.

Question 27Electronic data processing aptitude

A programmer needs to store a Boolean flag indicating whether an employee is active. Which data type is most appropriate for an EDP record field holding this flag?

  1. A variable-length text field of up to 255 characters
  2. A floating-point field with two decimal places
  3. A packed decimal field of ten digits
  4. A single-bit or one-character field with defined values for true and false Correct answer.

Explanation

A Boolean flag needs only two states, so a single bit or one-character field with agreed values is the most compact and unambiguous representation. Larger numeric or text fields waste storage and invite inconsistent values.

Question 28Electronic data processing aptitude

Which statement best describes the function of an assembler in an EDP environment?

  1. It converts high-level procedural statements into intermediate bytecode at run time.
  2. It executes each source statement immediately without producing an object file.
  3. It translates symbolic assembly language instructions into machine code before execution. Correct answer.
  4. It links separately compiled modules and resolves external references.

Explanation

An assembler converts mnemonic operation codes and symbolic operands into machine instructions and resolves addresses to produce an object module. Execution, linking, and high-level translation are separate steps performed by other components.

Question 29Electronic data processing aptitude

In a batch-processing EDP system, transactions are accumulated and processed together at a scheduled time. What is a principal advantage of this approach over immediate processing?

  1. It amortizes setup and I/O costs across many records, improving throughput for large volumes. Correct answer.
  2. It removes the requirement for a sorted transaction file.
  3. It guarantees that each transaction is reflected in the master file within seconds.
  4. It eliminates the need for any validation of input data.

Explanation

Batch processing groups work so that file opening, sorting, and sequential I/O costs are shared across many transactions, which raises throughput for high-volume routine work. The trade-off is delayed availability of results.

Question 30Electronic data processing aptitude

A record contains a numeric field defined as unsigned. What does this mean for the values it can hold?

  1. It stores only non-negative values, so the sign bit is not needed. Correct answer.
  2. It stores decimal fractions only.
  3. It stores both positive and negative values using two's complement.
  4. It stores only negative values.

Explanation

An unsigned field uses all bits for magnitude, so it represents zero and positive values only. This extends the positive range by one bit compared with a signed field of the same width.

Question 31Electronic data processing aptitude

An EDP operator notices that a report shows a total of items sold as 1,250 when the sum of the individual line quantities is 1,205. Which control is designed to detect this kind of discrepancy automatically?

  1. A check digit on each item code
  2. A parity bit on each transmitted byte
  3. A control total compared between the detail lines and the summary Correct answer.
  4. A range check on each quantity

Explanation

A control total is computed independently over the detail records and compared with the reported summary, exposing arithmetic or processing discrepancies. Check digits, parity, and range checks address different error classes.

Question 32Electronic data processing aptitude

In a computer system, what is the primary purpose of cache memory in the memory hierarchy?

  1. To store the operating system bootstrap permanently
  2. To hold recently or frequently used instructions and data close to the processor to reduce average access time Correct answer.
  3. To convert analog signals into digital data
  4. To provide permanent secondary storage for archived files

Explanation

Cache is a small, fast memory that keeps recently or frequently accessed items near the processor, exploiting locality to reduce average memory access time. It is volatile and far smaller than main or secondary storage.

Question 33Electronic data processing aptitude

A data-entry screen requires a postal code field to contain exactly five numeric characters. Which validation rule enforces this requirement?

  1. A picture or format check that requires five numeric positions Correct answer.
  2. A consistency check against the city field
  3. A check digit on the postal code
  4. A reasonableness check on the customer's age

Explanation

A picture or format check specifies the required pattern and length, so it rejects entries that are not exactly five numeric characters. The other checks verify different properties and would not enforce length and character type.

Question 34Electronic data processing aptitude

A file of 2,000 records is to be searched sequentially for a key that, on average, lies halfway through the file. Assuming a simple linear search from the first record, how many record comparisons are expected on average for a successful search?

  1. 2,000
  2. 500
  3. 1,000 Correct answer.
  4. 10

Explanation

A linear search examines records in order, so a successful search averages about half the file, which is 2,000 divided by 2, or 1,000 comparisons. The worst case would be 2,000.

Question 35Electronic data processing aptitude

A binary search is applied to a sorted array of 1,024 records. What is the maximum number of comparisons needed to determine whether a key is present?

  1. 1,024
  2. 11 Correct answer.
  3. 10
  4. 512

Explanation

Each comparison halves the remaining search interval, so the maximum number of comparisons is the number of halvings needed to reduce 1,024 entries to one. Since 2^10 equals 1,024, about 10 or 11 comparisons suffice depending on whether the final probe is counted, and 11 is the standard worst-case bound for 1,024 elements.

Question 36Electronic data processing aptitude

A program adds two 8-bit unsigned integers, 200 and 100, storing the result in an 8-bit register. What happens and why?

  1. The result is 100 because the second operand is discarded on overflow.
  2. The result is 300 because the register expands automatically to hold the carry.
  3. The result wraps to 44 because the sum 300 exceeds 255, causing unsigned overflow. Correct answer.
  4. The result is 44 because the operands are interpreted as signed values.

Explanation

An 8-bit unsigned register holds values from 0 to 255, so a sum of 300 cannot be represented and the stored result is 300 minus 256, which is 44, with a carry out. This is unsigned overflow, not signed interpretation.

Question 37Electronic data processing aptitude

A company stores customer records on a direct-access device and needs fast retrieval by customer number. Which file organization is most suitable when records are accessed in essentially random order by key?

  1. Sequential organization
  2. A file stored on magnetic tape in key order
  3. Hashed direct-access organization Correct answer.
  4. A file with no key field at all

Explanation

Hashed organization computes a storage address from the key, allowing near-constant-time retrieval for random access patterns. Sequential and tape-based organizations require scanning and suit batch processing better.

Question 38Electronic data processing aptitude

During program execution, a subroutine call occurs. What information must typically be saved so that execution can return correctly to the calling routine?

  1. The contents of the entire secondary storage device
  2. The source code of the calling routine
  3. The return address, along with any registers the caller needs preserved Correct answer.
  4. The value of the program's output files

Explanation

A call saves the return address, usually on a stack, and typically preserves registers or state that the caller expects to remain intact. This allows control to resume at the correct instruction after the subroutine finishes.

Question 39Electronic data processing aptitude

A data-processing application must ensure that a record is either completely written to disk or not written at all, even if a failure occurs mid-operation. Which technique supports this requirement?

  1. Writing the record directly with no logging
  2. Sorting the file before each write
  3. Logging the intended change and committing it atomically after successful completion Correct answer.
  4. Relying on a parity bit for the whole record

Explanation

Atomicity is achieved by writing a log or journal entry and committing the change only after the write completes successfully, so a failure can be rolled back or completed. This prevents partially written records from being treated as valid.

Question 40Electronic data processing aptitude

A relational table stores orders and must reference the customer who placed each order. What is the correct design to enforce that every order belongs to an existing customer?

  1. Place a foreign key on the customer identifier in the order table referencing the customer table's primary key Correct answer.
  2. Make the order number the primary key of the customer table
  3. Store the customer name as free text in the order table with no constraint
  4. Remove the customer identifier from the order table entirely

Explanation

A foreign key on the order table's customer identifier, referencing the customer table's primary key, ensures each order points to an existing customer. The database then rejects orders with unknown customers.

Question 41Electronic data processing aptitude

A disk drive has an average seek time of 8 ms and a rotational latency of 4 ms. Ignoring transfer time, what is the average time to locate a random block?

  1. 32 ms
  2. 8 ms
  3. 12 ms Correct answer.
  4. 4 ms

Explanation

Average access time is the sum of average seek time and average rotational latency, so 8 ms plus 4 ms equals 12 ms. Transfer time is excluded as stated.

Question 42Electronic data processing aptitude

A program uses a stack to evaluate a postfix expression. The expression is 5 3 + 2 *. What is the result?

  1. 13
  2. 16 Correct answer.
  3. 10
  4. 30

Explanation

Postfix evaluation pushes 5 and 3, then the plus pops them and pushes 8. It pushes 2, and the star pops 8 and 2 and pushes 16, which is the final result.

Question 43Electronic data processing aptitude

A data center uses RAID level 1 for a critical transaction log. What characteristic does this provide?

  1. Striping with parity, so capacity is maximized
  2. Mirroring, so data survives the failure of one disk in the pair Correct answer.
  3. No redundancy, so performance is highest
  4. Concatenation, so the disks appear as one large volume

Explanation

RAID 1 writes identical data to two or more disks, so a single disk failure does not lose data and reads can be served from either copy. It trades usable capacity for redundancy.

Question 44Electronic data processing aptitude

An EDP system converts a decimal value to binary-coded decimal (BCD). How is the decimal number 47 represented in packed BCD?

  1. 1011 1101
  2. 0100 0111 Correct answer.
  3. 0100 1011
  4. 0010 1111

Explanation

Packed BCD stores each decimal digit in a four-bit nibble, so 4 becomes 0100 and 7 becomes 0111, giving 0100 0111. Each nibble must hold a value from 0 to 9.

Question 45Electronic data processing aptitude

A program must sort a large file that does not fit entirely in main memory. Which approach is appropriate?

  1. External merge sort using sorted runs and multiway merging Correct answer.
  2. Quicksort applied to the entire file in memory at once
  3. Bubble sort applied directly to the disk file
  4. Selection sort with a single in-memory buffer of one record

Explanation

External merge sort creates sorted runs that fit in memory and then merges them in multiple passes, minimizing disk I/O. In-memory sorts cannot handle a file larger than memory, and quadratic sorts are impractical at scale.

Question 46Electronic data processing aptitude

A CPU executes instructions in a pipelined manner. What is the main benefit of instruction pipelining?

  1. Increasing the clock rate automatically without any design change
  2. Reducing the number of instructions a program must execute
  3. Eliminating the need for cache memory
  4. Overlapping the stages of successive instructions to increase instruction throughput Correct answer.

Explanation

Pipelining overlaps fetch, decode, execute, and other stages so that multiple instructions are in progress at once, raising throughput. It does not reduce the instruction count or remove memory hierarchy needs.

Question 47Electronic data processing aptitude

A file uses a hash function that maps keys into 50 buckets. After loading 500 records, one bucket contains 60 records while others are nearly empty. What is the most likely cause?

  1. An insufficient number of check digits
  2. A parity error in the bucket address
  3. Excessive rotational latency on the disk
  4. A poorly distributed hash function causing clustering Correct answer.

Explanation

Uneven bucket occupancy indicates the hash function does not spread keys uniformly, producing clustering and long overflow chains. Disk latency, check digits, and parity are unrelated to bucket distribution.

Question 48Electronic data processing aptitude

An indexed sequential file has a primary index that is sparse, holding one entry per block rather than per record. What is the effect of this design?

  1. Every record lookup requires exactly one index comparison and no block scan.
  2. Records must be stored in unsorted order to support the index.
  3. The index is smaller and fits in memory, but a block must be scanned after the index locates it. Correct answer.
  4. The index becomes larger than the data file itself.

Explanation

A sparse index stores only the highest key of each block, so it is much smaller than a dense index and can often remain in memory. The trade-off is that after locating the block, the program must search within it for the exact record.

Question 49Electronic data processing aptitude

A transaction-processing system uses two-phase locking. What guarantee does the protocol provide when all transactions follow it?

  1. Automatic recovery from power loss without logging
  2. Conflict serializability of committed transactions Correct answer.
  3. Guaranteed freedom from deadlock
  4. Elimination of all disk failures

Explanation

Two-phase locking, with a growing phase and a shrinking phase, ensures that any schedule of committed transactions is conflict serializable. It does not prevent deadlock, nor does it address hardware failures or recovery without logs.

Question 50Electronic data processing aptitude

A program must store a 40-bit unsigned integer value. Which storage approach preserves the value exactly?

  1. Use a 32-bit integer field with truncation
  2. Use a single-precision floating-point field
  3. Use an 8-bit character field
  4. Use a 64-bit integer field, since 40 bits fit without loss Correct answer.

Explanation

A 40-bit unsigned value exceeds the 32-bit range, so a wider field such as 64 bits stores it exactly. Truncation, single precision, and eight-bit fields cannot represent all 40-bit values without loss.