Katharina Harrer laughed nervously as she unloaded her groceries, astonished at the sight of a computer terminal, complete with flashing orange digits and a laser beam, sitting where the old supermarket cash register had been.

"I've seen it on TV, but here . . . I didn't know they had them here," she said, gawking at the machine and talking rapidly. "It's great if the machine doesn't cheat. The girl doesn't have to ring the buttons, all she has to do is just pack it in. It's faster."

Cash registers, the big, ringing machines with fullblown chests, buttons for every digit of every price and snap-zing cash drawers are becoming relics in many Washington stores, including the Giant supermarket at Newark Street and Wisconsin Avenue NW where Harrer did her shopping the other day.

The machines that cashiers have poked with fingers and banged with fists since the early 1900s are being replaced increasingly here by computers that read an identifying code of black lines and white spaces on groceries or other retail items, print the name and price of every item on receipts, take stock of what and how much is being sold and then instantly order new supplies.

At the eight Sears stores and six Toys-R-Us outlets in the Washington area, the cash register's replacement is a pencil-shaped electronic wand that is connected to a computer. When passed over a new toy airplane, for example, the wand shoots a beam of light across the toy's coded tag to identify the item for the computer, which then determines the price and completes the sale by calculating the change due the customer.

At 32 Giant Food stores in the area, a new register-computer system has laser beam scanners imbedded in the checkout counters. These read the striped code on every item and the register gives a quick beep to indicate that it has found the price of the item in its memory banks.

The computer then flashes the name and price of the item on an electronic readout screen in front of the customer. Fegetables and fruit cannot be tagged with the product codes, but the display screen also flashes the weight of produce when it is placed on a counter scale attached to the system.

Computer technology also is replacing old fashioned cash registers at a growing number of area restaurants, particularly fast-food, high-volume operations.

On such register computers, hamburgers have a special button, gin and tonics have a special button: Delmonico steak, baked potato, or any other item a restaurant has to offer is specified by name - each on a separate button. A quick touch of the buttons and the computer instantly produces a statement telling the customer exactly what he had to eat or drink and what it cost him.

Giant Food is the acknowledged supermarket industry leader in converting to computerized checkout, and from both clerks and company executives, the system has received mostly praise.

"We have found that customers like it so well in the supermarkets that every store picks up business and holds it," said Donald Buchanan, vice president of Giant. "I have a letter here from a Giant shopper in a town where we haven't converted yet and the letter says the whole town feels slighted because we didn't put the new system in there. It's become a matter of civic pride. Everybody wants it."

Initial customer reaction is mixed, however, at the Giant store at Wisconsin Avenue and Newark Street, where the District of Columbia's first supermarket register-computer system was installed in October.

"It's like a toy, science fiction," said Maria Monterroso, a student at Wilson High School. "The line goes more quickly, too, so I come here more often."

"The best thing about it is that there isn't any more padding," said a well-dressed woman who didn't want her name in the newspaper. "You know they sometimes ring up too much or too little on the cash registers. I used to watch them ring up every item."

One gray-haired shopper, Sophia Miles, was not, however, taken with the new machinery.

"Why do they need to put these things in the store?" she asked. "It is too slow. There is that beeping all the time. There was nothing wrong with the way they were doing it. I would come in here more often if they got back the old cash register."

Bob Caudell, the store manager and a booster of the computer system, said elderly shoppers are having the hardest time adjusting to the new checkout system.

"They don't trust it," he said. "They're not interested in how it works . . . it seems to upset them."

Kathleen O'Reilly, executive director of the Consumer Federation of America, says that customers of stores using the new machines have found several incorrect prices on their shopping receipts as a result of mistakes by the computer.

Consumer groups have complained in the past that price tags are not on every item in computerrized stores. To save money, some of these stores have stopped stamping each package with its price in the traditional purple ink used by supermarkets. Instead, these stores have relied on signs or price tags on shelves. But without prices on every item, consumers have complained that it difficult to compare products for price and value.

Giant's computerized stores in the Washington area now have price tags attached to shelves below each item, which seems to be acceptable to customers. A 1976 study by Michigan State University found that in computerized supermarkets where prices weren't displayed, customers were leaving the stores to shop elsewhere at a 16 per cent higher rate than would otherwise have been the case.

O'Reilly said said that five states - Connecticut, Michigan, California, Massachusetts and New York - have passed laws requiring supermarkets to put price tags on every item.

Despite its critics, the computerized checkout system has won the acclaim of store managers and industry executives who see it as an opportunity to reduce their labor costs by decreasing the number of employees who weigh fruits and vegetables, stamp prices on food packages and who work as cashiers.

"Anytime management can cut labor costs it is going to mean savings for shoppers," said Harry Sullivan of the Food Marketing Institute, a trade association representing supermarket chains and wholesale food distributors.

Under union contracts, cashiers at Giant and other stores using the new checkout system cannot lose their jobs because of automation. Salaries paid to cashiers have not been cut due to the computers, according to Giant officials.

Since 1973 about 225 stores across the nation have installed computer equipment. The number of restaurants using computer system cash registers, which have a button for every item, is far greater but actual figures are not available.

Manufacturers of packaged food products get their product code symbols and numbers from District Codes Inc., an Alexandria firm. The symbol can cost rhe manufacturer as much as $10,000 or as little as $250, depending on the amount of the product that is sold annually.

A company spokeswoman for district Codes said 5,700 firms have been assigned symbols so far and 85 per cent of the packages in stores today, including baseball cards and magazines have a product code on them.

The first five numbers in the 10 number code identify the manufacturer of the product, such as Lipton's. The last five numbers identify the product, such as iced tea.

Prices can be changed instantly in the computer system on instructions from a main computer. Giant Food's main computer in Landover currently makes price changes during the night by connecting with computers in Giant's branch stores by telephone.

After instructing the store's computers to change the prices, the main computer also orders new price tags for store shelves. The new price tags are then put on the shelves manually by store employees.

When the stores open the next day the branch store computer reads the product code of Lipton Iced Tea, for example, and charges the new price.

"I'll tell you what amazes me about this system, the best part," said Giant vice president Buchanan. "Everyday we can know what we sold in every store in the area. If we have a sale today I can know how much we sold by tonight. You can't imagine how that helps us run the business . . . it's unbelievable, that's the year 2000."